Expresiones algebraicas de suma, resta y valor
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This document provides an overview of algebraic expressions. It defines algebraic expressions as combinations of numbers and letters related through arithmetic operations. Examples of terms that make up algebraic expressions are given, such as monomials, binomials, and polynomials. The document then discusses how to perform operations like addition, subtraction, multiplication, and division on algebraic expressions. It also explains how to evaluate algebraic expressions by substituting numeric values for variables and provides examples. Finally, it covers factoring algebraic expressions using notable products like the difference and sum of squares.
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3) Write these two numbers above and below the box to factor the expression.
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This slideshow will show you how to factor polynomials using:
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This document discusses basic algebraic expressions and provides recommendations for working with them. An algebraic expression is a combination of numbers and letters related through basic arithmetic operations. It is important to have a solid understanding of properties, operations, and sign rules when working with algebraic expressions. Expressions can be analyzed based on their terms, degrees, and other characteristics in order to perform operations like factoring. Examples are provided to demonstrate summations, subtractions, multiplications, divisions, and other operations with monomials, binomials, trinomials, and polynomials.
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This document discusses algebraic expressions, factorization, and radicalization. It covers topics such as:
- Defining algebraic expressions as combinations of letters and numbers connected by arithmetic symbols.
- Methods for adding, subtracting, multiplying, and dividing algebraic expressions.
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- Factorizing expressions using notable products like the difference and sum of squares.
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The document provides examples and explanations of operations involving polynomials, including:
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3) Dividing polynomials using tiles to represent the division operation and finding quotients and remainders.
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The document provides step-by-step instructions for factorizing a quadratic trinomial using the grouping method. The method involves: 1) drawing an X and writing the middle and first times last terms; 2) finding two factors whose sum is the middle term and product is the first times last; 3) writing the factors on either side of the X and dividing by the leading coefficient; 4) plugging the factors into the (x + )(x + ) format and moving the denominator in front of the x terms. When completed, the factorization is obtained.
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Algebraic expressions can be formed using variables, constants, and mathematical operations. Variables represent letters that can take on any value, while constants represent fixed numbers. There are different types of algebraic expressions including monomials, binomials, and trinomials. The value of an algebraic expression can be found by substituting values for the variables and simplifying. Identities are equations that are always true regardless of the values of variables. Common identities include (a+b)2, (a-b)2, and a2 - b2.
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This document provides an overview of squares and square roots including:
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- Perfect squares being numbers where the square root is also a whole number
- Patterns involving squares such as even/odd properties and formulas for decomposing squares
- Methods for finding squares including the diagonal method and using formulas like (a + b)2
- Pythagorean triplets being sets of three numbers that satisfy the Pythagorean theorem when used as sides of a right triangle
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The document discusses various methods for factoring quadratic expressions and solving quadratic equations by factoring. These include:
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The document provides examples of factoring quadratic expressions of the form a^2 +/- b^2 into the form (a +/- b)(a -/+ b). It demonstrates factoring several quadratic expressions using this method, including expressions with coefficients other than 1. It also introduces a formula for factoring expressions of the form a^2 + 2ab + b^2 and applies this formula to one example. Finally, it factors one expression where the middle term is negative by distributing the negative sign appropriately.
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The document discusses factoring the difference of two squares. It states that the factors of the difference between two squares are the product of the sum and difference of the two numbers. It then provides examples of factoring different expressions involving the difference of two squares in three steps: 1) take the square root of each term, 2) use the results to form the sum and difference of the numbers, and 3) write the factored expression as the product of the sum and difference.
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1) It explains how to factor polynomials by finding the greatest common factor (GCF).
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3) It shows how to factor trinomials of the form ax2 + bx + c by finding factors of a, c whose products and sums satisfy the polynomial.
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The document explains and provides examples of how to factor quadratic expressions using the "x-box" method. This method involves drawing an x-box with the coefficients of the expression and identifying the greatest common factor and two binomial factors that multiply to the original expression. Three examples are provided and worked through step-by-step to demonstrate how to set up and solve factoring problems using the x-box method.
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The document provides instructions for factoring quadratic trinomials using 4 examples. It explains that you write the trinomial as two parentheses, factor the constant term into the parentheses, then check that the factors give the middle term of the original expression when multiplied out. The process involves 4 steps and is demonstrated factoring expressions like x^2 + 10x + 24 and x^2 - 8x + 15.
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Commenting and Liking our Slideshow will help us a lot! Please support us by doing so.
This slideshow will show you how to factor polynomials using:
* Greatest Common Monomial Factor
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* Factor by Grouping
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Expresiones algebraicas de suma, resta y valor
- 1. Expresiones algebraicas. Nombre:Niccol Daniel Apellido: Rodríguez sabaleta Seccion:0102 Fecfa:26/3/21
- 2. Desarrollo • Expresiones algebraicas: • Una expresión algebraica es una combinación de números y letras relacionados mediante operaciones aritméticas; adición, sustracción, multiplicación, división y potenciación. La expresión algebraica está conformada por TÉRMINOS. Palabras Clave: Monomio, Binomio, Trinomio, Polinomio, Identidad, Ecuación. • Por ejemplo: 8X-78Z • (3X-1) / (9X-2)
- 3. Suma de Expresiones algebraicas • Para sumar dos o mas expresiones algebraicas con uno o mas términos sede ven reunir todos los términos semejantes que existan, en uno solo. • 1) 3𝑥2 + 2 𝑥2 + 2 𝑥 + 2 2) 2 𝑋2 + 3𝑋 + 2 • 2𝑥3 +𝑥2 +5 x+5 4𝑋2 + 5 𝑋 + 6 6𝑋2 + 8𝑋 + 8 5𝑿𝟑 + 𝟑𝑿𝟐 + 𝟖𝑿 + 𝟕
- 4. Resta de Expresiones algebraicas • Para restar se suma o se resta los coeficiente de cada monomio y se coloca la misma variable. • 1) 2𝑥3 − 4𝑥2 + 3𝑥 − 2 2) 4𝑋2 − 2𝑋 + 3 • 𝑥3 +𝑥2 − 2𝑥 + 4 −5𝑋2 + 5 𝑋 − 5 3𝑋3 − 2𝑋2 + 𝑋 − 2 −𝑋2 + 3𝑋 − 2
- 5. Valor numérico de expresiones algebraicas • Consisten en de un polinomio la variable x por el numero entero sea (+ o -) es decir. • 𝑝 𝑋 = 2𝑋2 + 3𝑋 − 5 𝑃𝑂𝑅 𝑋 = −2 • 2(−2)2 + 3 −2 − 5 = • 2.4 − 6 − 5 = 8 − 11 = −3 • 𝑄 𝑋 = 3𝑋3 − 2𝑋2 + 𝑋 − 5 𝑃𝑂𝑅 𝑋 = 2 • 𝑄 2 = 3(2)3 − 2(2)2 + 2 − 5 • 3.8 − 2.4 + 2 − 5 • 2,4 − 8 + 2 − 5 = 13 Q(X)=13
- 6. 8𝑋5 − 2𝑋4 − 18𝑋4 − 𝑋2 + 19𝑋 − 10 Multiplicación de expresiones algebraicas • Consiste en realizar una operación entre los términos llamado multiplicando y multiplicador para encontrar un tercer termino llamado producto. • 1) 2𝑋2 + 2𝑋2 − 3𝑋 − 5 𝑃(𝑋) 2) 𝑝 𝑥 = 2𝑥2 − 3 + 2 𝑦 𝑞 𝑥 = 3𝑥 + 5 • 4𝑋2 − 5𝑋 + 2 𝑄 𝑋 hallar P(x) . Q(x)= • 4𝑋3 + 4𝑋2 − 6𝑋 − 10 𝑃 𝑋 . 𝑄 𝑋 2𝑥2 − 3𝑥 + 2 • −10𝑋4 − 10𝑋2 + 1.5𝑋2 + 2.5𝑋 3𝑥 + 5 • 8𝑋5 + 8𝑋4 − 12𝑋2 − 20𝑋2 10𝑥2 − 15𝑥 + 10 • 6𝑥3 − 9𝑥2 + 6𝑥 • 6𝑋3 + 𝑋2 + 9𝑋 + 10
- 7. Divisiones de expresiones algebraicas • Consiste en la misma devoción aritmética; p(x)=dividendo y q (y)= divisor; para encontrar el resto le explicaremos. • 4𝑋2 − 2 + 8 2𝑋 + 4 18𝑥5 𝑌5 𝑍2 • −4𝑥2 − 8𝑥 2𝑥 − 5 2𝑋2 𝑌2 𝑍1 • −10𝑥 + 8 Dividimos, se copia las variables y se los exponentes • +10𝑥 + 20 • +28 • 9𝑥2 𝑌 𝑍 D 4 O 2𝑑 R 2𝑐
- 8. Producto notables de expresiones algebraicas • Son multiplicaciones especiales entre expresiones algebraicas y si expresa asi: El cuadrado de una suma algebraica y se resuelve así; • (𝑎 + 𝑏)2 = 𝑎2 + 2 𝑎 𝑏 + 𝑏2 2)(5𝑥 − 2)2 =(5𝑥)2 − 2.5𝑥. 2 + 22 • (𝑎 − 𝑏)2 = 𝑎2 − 2 𝑎 𝑏 − 𝑏2 𝑎 𝑏 • Ej:(2𝑥 + 3)2 = (2𝑥)2 + 2.2 𝑥. 3 + 32 • 𝑎 𝑏 = 4𝑥2 + 12𝑥 + 9 25𝑥2 − 20𝑥 + 4
- 9. Factorización de expresiones algebraicas • Consiste en que cada producto notable es una factorización es decir la viceversa. • 4𝑥2 + 12𝑥 + 9 = (2𝑥 + 3)2 2)otros productos notables • 25𝑥2 − 20𝑥 + 4 = (5𝑥 − 2)2 𝑎 + 𝑏 𝑎 − 𝑏 = 𝑎2 − 𝑏2 • 𝑥2 − 4 = 𝑥 − 2 𝑥 − 2 𝑥 + 2 𝑥 − 2 = 𝑥2 − 22 • 4𝑥2 − 2𝑥 − 6 = 2𝑥 + 2 2𝑥 − 3 =𝑥2 − 4 • 𝑥3 + 9𝑥2 + 27𝑥 + 27 = (𝑥 + 3)3 2𝑥 + 2 2𝑥 − 3 = 4𝑥2 − 6𝑥 − 4𝑥 − 6 •