Lesson 98
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This document provides a lesson on multiplying binomials using the FOIL method. It begins with a review of multiplying monomials and practicing multiplying binomials. It then introduces binomials as expressions with two terms and characteristics. The FOIL method for multiplying binomials is explained as multiplying the First terms, Outside terms, Inside terms, and Last terms. Examples of using FOIL to multiply binomial expressions like (x+2)(x+5) are provided. The lesson concludes with assigning homework on multiplying binomials using FOIL.
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Multiplying binomials
This document discusses multiplying binomial expressions using the distributive property. It explains that the distributive property, a(b + c) = ab + ac, allows one to multiply a binomial by distributing the first term of the second binomial over the terms of the first binomial. This results in multiplying the first terms, outer terms, inner terms, and last terms, which is remembered with the acronym FOIL. An example problem demonstrates using FOIL to multiply two binomials.
Using Foil To Multiply Binomials
The document provides an explanation of how to use the FOIL method to multiply binomial expressions. It defines what a binomial is, explains that FOIL is a mnemonic for the steps of First, Outer, Inner, Last. It then demonstrates how to use FOIL by working through simple examples without variables and a more complex example with variables, showing the pairing and multiplication of terms according to the FOIL steps. Additional resources on FOIL multiplication are provided.
Instructional Materials in Mathematics
The document describes several instructional materials for teaching mathematics concepts:
1. Grid board, modified geoboard, fraction slider, and number slider are used to teach perimeter, area, fractions, and integers.
2. Algebra tiles are used to model linear expressions, solve equations, and simplify polynomials.
3. Fraction pie relates fractions to circle circumference and parallelogram perimeter.
4. A powerpoint on perimeter and area teaches calculating these values for polygons and circles.
5. Models of the platonic solids, sphere, and archimedean solids are used to investigate their properties like surface area and volume.
Multiplication of binomials
This document describes the FOIL method for multiplying binomial expressions. FOIL is an acronym that represents multiplying the First, Outer, Inner, and Last terms of each binomial: first multiply the first terms, then the outer terms, then the inner terms, and finally the last terms. The document provides examples of using FOIL to multiply (3x+2)(4x+1), (x+4)(5x+2), and (3x+2)(4x+1).
7.6 notes b
1) The document defines polynomials as expressions that can be written as the sum of one or more monomials. A monomial is the product of a number, variable, and nonnegative integer powers.
2) The degree of a monomial is the sum of the exponents of its variables. The degree of a polynomial is the highest degree among its monomial terms.
3) Polynomials are classified by degree, with linear having degree 1, quadratic degree 2, cubic degree 3, and so on. Basic arithmetic with polynomials involves combining like terms.
Multiplying polynomials powerpoint
This document provides instructions for multiplying polynomials using three methods: the distributive property, FOIL (First Outer Inner Last), and the box method. FOIL is only used when multiplying two binomials, involving multiplying the first, outer, inner, and last terms of each binomial. The distributive property and box method can be used for any polynomials. Examples are provided to demonstrate multiplying polynomials step-by-step using each method.
January 29 30
The document provides practice problems on simplifying monomial expressions and dividing monomials. It begins with examples of dividing monomials using the property that when dividing powers with the same base, you subtract the exponents. It then provides practice problems for students to divide monomial expressions and simplify expressions using exponent properties. Sample problems are worked through step-by-step as examples.
Feb6
The document discusses various methods for multiplying binomial expressions, including the distributive property, the box method, and the F.O.I.L. (First, Outer, Inner, Last) method. It also covers patterns that emerge when multiplying binomials mentally and how the signs of terms impact the results. Practice problems are provided to help solidify these skills.
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Multiplying binomials
This document discusses multiplying binomial expressions using the distributive property. It explains that the distributive property, a(b + c) = ab + ac, allows one to multiply a binomial by distributing the first term of the second binomial over the terms of the first binomial. This results in multiplying the first terms, outer terms, inner terms, and last terms, which is remembered with the acronym FOIL. An example problem demonstrates using FOIL to multiply two binomials.
Using Foil To Multiply Binomials
The document provides an explanation of how to use the FOIL method to multiply binomial expressions. It defines what a binomial is, explains that FOIL is a mnemonic for the steps of First, Outer, Inner, Last. It then demonstrates how to use FOIL by working through simple examples without variables and a more complex example with variables, showing the pairing and multiplication of terms according to the FOIL steps. Additional resources on FOIL multiplication are provided.
Instructional Materials in Mathematics
The document describes several instructional materials for teaching mathematics concepts:
1. Grid board, modified geoboard, fraction slider, and number slider are used to teach perimeter, area, fractions, and integers.
2. Algebra tiles are used to model linear expressions, solve equations, and simplify polynomials.
3. Fraction pie relates fractions to circle circumference and parallelogram perimeter.
4. A powerpoint on perimeter and area teaches calculating these values for polygons and circles.
5. Models of the platonic solids, sphere, and archimedean solids are used to investigate their properties like surface area and volume.
Multiplication of binomials
This document describes the FOIL method for multiplying binomial expressions. FOIL is an acronym that represents multiplying the First, Outer, Inner, and Last terms of each binomial: first multiply the first terms, then the outer terms, then the inner terms, and finally the last terms. The document provides examples of using FOIL to multiply (3x+2)(4x+1), (x+4)(5x+2), and (3x+2)(4x+1).
7.6 notes b
1) The document defines polynomials as expressions that can be written as the sum of one or more monomials. A monomial is the product of a number, variable, and nonnegative integer powers.
2) The degree of a monomial is the sum of the exponents of its variables. The degree of a polynomial is the highest degree among its monomial terms.
3) Polynomials are classified by degree, with linear having degree 1, quadratic degree 2, cubic degree 3, and so on. Basic arithmetic with polynomials involves combining like terms.
Multiplying polynomials powerpoint
This document provides instructions for multiplying polynomials using three methods: the distributive property, FOIL (First Outer Inner Last), and the box method. FOIL is only used when multiplying two binomials, involving multiplying the first, outer, inner, and last terms of each binomial. The distributive property and box method can be used for any polynomials. Examples are provided to demonstrate multiplying polynomials step-by-step using each method.
January 29 30
The document provides practice problems on simplifying monomial expressions and dividing monomials. It begins with examples of dividing monomials using the property that when dividing powers with the same base, you subtract the exponents. It then provides practice problems for students to divide monomial expressions and simplify expressions using exponent properties. Sample problems are worked through step-by-step as examples.
Feb6
The document discusses various methods for multiplying binomial expressions, including the distributive property, the box method, and the F.O.I.L. (First, Outer, Inner, Last) method. It also covers patterns that emerge when multiplying binomials mentally and how the signs of terms impact the results. Practice problems are provided to help solidify these skills.
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This lesson plan outlines how to teach 7th grade students to multiply polynomials. It includes objectives, subject matter, procedures, and assessment. Students will learn to multiply monomials, binomials, and polynomials with multiple terms using distribution and combining like terms. Examples are provided for multiplying different combinations of monomials and binomials. A review, lesson, and problem solving section are included in the procedures. The assessment evaluates students' understanding of defining polynomials and multiplying different polynomial expressions.
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1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
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1. There are three methods for multiplying polynomials: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. FOIL is only used when multiplying two binomials.
2. The worked example uses FOIL and the box method to multiply (3x - 5)(5x + 2), getting 15x^2 - 19x - 10.
3. Multiplying polynomials with variables of differing degrees, like (2x - 5)(x^2 - 5x + 4), requires using the distributive property rather than FOIL.
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1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
Unit 1 test 2.9 notes a
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
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To multiply polynomials, one can use the distributive property by distributing one polynomial over the other, the FOIL method for multiplying binomials by multiplying the First, Outer, Inner, and Last terms, or the box method which involves drawing a box and distributing the terms. All three methods yield the same result but use different approaches to arrive at the final polynomial. The document provides examples of multiplying polynomials using each method along with step-by-step explanations and instructions.
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mr. amato's class presentation
to satisfy tech. requirement i have demonstrated ability to create, enhance and manipulate a slide presentation
Foil
The document provides instructions for multiplying polynomials using three methods: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. FOIL is only used when multiplying two binomials, while the distributive property and box method can be used for any polynomials. Examples are provided to demonstrate multiplying polynomials of varying complexities using each method. Students are encouraged to practice the methods and choose the one they find easiest.
multiplicació polinomis amb FOIL
The document provides instructions for multiplying polynomials using three methods: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. FOIL is only used when multiplying two binomials, while the distributive property and box method can be used for any polynomials. Examples are provided to demonstrate multiplying polynomials of varying complexities using each method. Students are encouraged to practice the methods and choose the one they find easiest.
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1. The document discusses various algebra topics for the day including make-up tests, expanding and factoring polynomials, and polynomial long division.
2. It emphasizes that factoring polynomials is important as it is often the first step in solving problems, and describes different methods for factoring including finding all terms that were multiplied together.
3. The document also covers the processes of expanding polynomials through distribution, and dividing polynomials using both long division and dividing out common monomial factors. Examples are provided for each topic.
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Detailed Lesson Plan in Mathematics
This lesson plan outlines how to teach 7th grade students to multiply polynomials. It includes objectives, subject matter, procedures, and assessment. Students will learn to multiply monomials, binomials, and polynomials with multiple terms using distribution and combining like terms. Examples are provided for multiplying different combinations of monomials and binomials. A review, lesson, and problem solving section are included in the procedures. The assessment evaluates students' understanding of defining polynomials and multiplying different polynomial expressions.
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1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
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1. There are three methods for multiplying polynomials: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. FOIL is only used when multiplying two binomials.
2. The worked example uses FOIL and the box method to multiply (3x - 5)(5x + 2), getting 15x^2 - 19x - 10.
3. Multiplying polynomials with variables of differing degrees, like (2x - 5)(x^2 - 5x + 4), requires using the distributive property rather than FOIL.
Unit 1 test 2.9 notes b
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
Unit 1 test 2.9 notes a
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
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Polynomials are algebraic expressions consisting of variables, constants, and exponents combined using operations like addition, subtraction, multiplication, and division. They are classified based on the number of terms as monomials, binomials, or trinomials. The degree of a polynomial refers to the highest exponent present. Common polynomial operations include adding and subtracting like terms, multiplying polynomials according to distributive properties, and using long division to divide polynomials. Division of polynomials does not always result in another polynomial.
Lesson 7-7FOILPPT.ppt
To multiply polynomials, one can use the distributive property by distributing one polynomial over the other, the FOIL method for multiplying binomials by multiplying the First, Outer, Inner, and Last terms, or the box method which involves drawing a box and distributing the terms. All three methods yield the same result but use different approaches to arrive at the final polynomial. The document provides examples of multiplying polynomials using each method along with step-by-step explanations and instructions.
March 17, 2015
Today's class will include a warm-up, factoring polynomials using the greatest common factor (GCF) method and factoring by grouping, and Khan Academy assignments due tonight. Students should show all their work to receive credit for class work involving factoring polynomials using GCF and grouping methods.
Multiplying polynomials
This document discusses multiplying polynomials. It begins by explaining how to multiply terms using the product rule and combining like exponents. It then shows how to multiply a monomial by a binomial using the distributive property. Examples are provided of multiplying a monomial with a binomial, two binomials, and an example for the reader to try on their own. The document concludes by encouraging the reader to ask their teacher if they have any other questions before taking a formative assessment.
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This document reviews three methods for multiplying polynomials: the distributive property, FOIL method, and box method. It provides examples of multiplying binomials like (2x + 3)(5x + 8) and (y + 4)(y - 3) using each method. The key steps of each method are defined, including the FOIL acronym for the order of multiplying terms in binomials.
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The document provides information and examples about solving quadratic equations by completing the square. It begins with reviewing solving quadratics by factoring, graphing, and square roots. Then it introduces completing the square as a fourth method. Examples are provided to show how to identify the value to add inside the square and rewrite the equation in factored form. Students are assigned practice problems in pairs to work through applying this new method.
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The document provides instructions for multiplying polynomials using three methods: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. FOIL is only used when multiplying two binomials, while the distributive property and box method can be used for any polynomials. Examples are provided to demonstrate multiplying polynomials of varying complexities using each method. Students are encouraged to practice the methods and choose the one they find easiest.
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Are you scared of that algebraic sums? Just view this presentation an you can learn about each and every algebraic identities. Just view this and Now take full marks in your tests..
DLLWeek1_3.docx
This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, procedures, and reflections for lessons on factoring polynomials. Specifically, it covers factoring polynomials with common monomial factors, the difference of two squares, the sum and difference of two cubes, perfect square trinomials, and general trinomials. The procedures describe reviewing previous lessons, presenting new material with examples, discussing concepts, practicing skills, developing mastery through activities, and assessing learning. Reflections include the number of students who achieved mastery and require remediation on the topics.
March 17, 2014
1. The document discusses various algebra topics for the day including make-up tests, expanding and factoring polynomials, and polynomial long division.
2. It emphasizes that factoring polynomials is important as it is often the first step in solving problems, and describes different methods for factoring including finding all terms that were multiplied together.
3. The document also covers the processes of expanding polynomials through distribution, and dividing polynomials using both long division and dividing out common monomial factors. Examples are provided for each topic.
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This document contains notes from a math lesson on factoring polynomials. It discusses factoring by grouping, where common terms are factored out and then grouped together. It also discusses factoring polynomials into quadratic form when they are raised to higher powers. Examples are provided for both techniques, along with exercises for students to practice factoring by grouping. It concludes with a challenge problem involving factoring a polynomial equation related to the volume of a jewelry box in order to determine its dimensions.
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This document provides an overview of key concepts in college algebra including variables, algebraic expressions, polynomials, and methods for combining and multiplying algebraic terms. It defines variables, monomials, binomials, trinomials, and polynomials. It explains how to add, subtract, and multiply polynomials using properties of exponents and the distributive property. It introduces special product formulas that are useful for multiplying common polynomial expressions like (a + b)2 and (a - b)(a + b). Examples are provided to demonstrate each concept.
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Lesson 98
- 1. Lesson 98: Multiplication of Binomials (FOIL) Teacher: Miss. Haibeh
- 2. Review: Last week, we learned about Multiplying a Monomial by a Monomial. Let us practice some questions for a review: 1. (3x²)(-4x) 2. (-2a²b²)(-3ab) 3. (4x^4y)(-2xz) 4. (-3x³y)(-2xy)
- 3. Warm up: Here are some questions, use any method you find suitable to get final answer: 1) 3 x ( 2 + 3 ) = 2) 9 x ( 2 + 3 ) = 3) ( 2 + 3 ) x ( 3 + 9) =
- 4. What are Binomials A binomial is a mathematical expression with two terms. Below are some examples of binomials. Example: 3x+5 Characteristics of Binomials: ◦ Must have two terms. ◦ If the variables are the same, then the exponents must be different. ◦ Exponents must be whole positive integers. They cannot be negatives or fractions.
- 5. Multiplying Binomials (FOIL) Originally, in the warm up we used a different method called the distributive method. Distributive method can be used for all polynomials (adding, subtracting etc). However there is a method that can be used only for the multiplying binomials and cannot be used for other sets of multiplications. This method is called FOIL When you hear the word FOIL, what comes to mind first?
- 6. Is this the image that comes to mind..
- 7. How do you think the FOIL method is applied? Try this out: (x+3)(x+2) FOIL stands for First Outside Inside La
- 9. Few Examples: 1. (x+2)(x+5) 2. (x-4)(x+5) 3. (x+1)(x+3) 4. (x+3)(x-10)
- 10. Wrap Up: Binomials can be multiplied using the FOIL method to keep track of the operations. Homework Assignment. See you all tomorrow!
Editor's Notes
- Explanation – coefficient and variables and exponents Combining like terms.
- Make student ‘discover the lesson’ 10 mintues
- http://www.regentsprep.org/regents/math/algebra/AV3/Smul_bin.htm