Algebraic Expressions PPT.pptx
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Numeric expressions contain only numbers, while algebraic expressions contain variables that represent unknown numbers. An algebraic expression has three parts: a variable, a coefficient, and a constant. A monomial is an algebraic expression with only one term, while a polynomial has two or more terms. To evaluate an algebraic expression, substitute values for the variables and simplify using order of operations. Expanding an expression uses the distributive property to multiply terms within parentheses. Simplifying combines like terms, which have the same variables raised to the same powers.
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Operations on Polynomials
To multiply polynomials, you can use the distributive property and properties of exponents. When multiplying monomials, group terms with the same bases and add their exponents. When multiplying binomials, use FOIL or distribute one binomial over the other. For polynomials with more than two terms, you can distribute or use a rectangle model to systematically multiply each term.
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Step 1) Solve one equation for one variable.
Step 2) Substitute the expression from Step 1 into the other equation.
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- 2. What is the difference between a numeric expression and an algebraic or variable expression? Numeric Expression Algebraic Expression -3 + 2 + 4 – 5 -3x + 2y – 4z - 5
- 3. An algebraic or variable expression consists of three parts • Variable • Coefficient • Constant
- 4. The variable is a symbol or letter that represents a number. What are the variables in the expression below? - 4x + 3y - 8z + 9
- 5. The coefficient is the number that multiplies the variable. More plainly, it is the number in front of a variable. What are the coefficients in the expression below? - 4x + 3y - 8z + 9
- 6. The constant is any term that does not have a variable. What is the constant in the expression below? - 8 + 5y + 3x
- 7. An algebraic expression may be classified as a monomial. A monomial only has one term. It is an expression consisting of a number and a variable or the product of numbers and variables that have whole number exponents. A monomial cannot have a variable in the denominator.
- 8. Comprehension Check Identify the expressions that are not monomials. Justify your answer. -4xy xy/4 4 + x 0.7x-1 y/x
- 9. An algebraic expression can also be classified as a polynomial which is an expression that consists of more than one term. Two types of polynomials are binomials and trinomials. A binomial has two terms. Ex: 3x + 4 A trinomial has three terms. Ex: 4a2 + 3a + 7
- 11. Evaluating an algebraic/variable expression involves solving it when the variable/s in that expression are given a numeric value. To evaluate a variable expression, you first replace each variable with the numbers to which they are equal. Then you use the order of operations to simplify. Remember! Please Excuse My Dear Aunt Sally ParenthesesExponents x / + - (Multiplication and Division are done in the order in which they appear. Which ever operation appears first, is done first. The same applies for addition and subtraction when both operations are found within a problem.)
- 12. EVALUATING EXPRESSIONS EXAMPLES Example 1 Evaluate 4y – 15 for y = -9 • 4y - 15 • 4(-9) – 15 • -36 – 15 = - 51 Example 2 Evaluate 3ab + c2 for a = 2, b =-10, and c = 5. • 3ab + c2 • 3(2)(-10) + 52 • -60 + 25 =-45 Example 3 Evaluate 6(g + h) for g=8 and h = 7. • 6(8 + 7) • 6 (15) = 90
- 13. LET’S PRACTICE! • Evaluate each expression for x = -2, y = 3 and z =-10 xyz 8y + z2 z/5 + 2 4y – x 2z + xy 9 + y2 4xy – z -5(y + z)2 x
- 14. EXPANDING ALGEBRAIC EXPRESSIONS Using the Distributive Property
- 15. Distributive Property Expanding an algebraic expression involves using the distributive property. When the distributive property is used, you multiply the quantity in front(or sometimes in the back) of of the parentheses by each term in the parentheses. Remember to use integer rules for multiplication (if multiplying same signs – answer is positive, if multiplying different signs – signs – answer is negative). Examples 4(2x – 3) = 8x - 12 -5(4x – 9)= -20x +45 0.2 (3b – 15c) = .6b – 3c - (5x – 3y + 8z) = -5x + 3y – 8z (2x + 5)7 = 14x + 35 ½ (6e + 8f – 14g) = 3e + 4f – 7g
- 16. LET’S PRACTICE! EXPAND EACH EXPRESSION • -3(x + 5) = • 2(-8x + 10) = • -(4x – 3y + 7z) = • -8(-2x – 3 ) = • 1/3(6x – 45) =
- 17. SIMPLIFYING ALGEBRAIC EXPRESSIONS Distributive Property & Combining Like Terms
- 18. Simplifying expressions involves combining like terms. Like Terms are monomials that have variables raised to the same powers. What terms are like terms with 4a2b? -16ab 3ab2 -7a2b 11a2b2 5a2b
- 19. When combining like terms, you group like terms together. Then you use addition rules to combine the coefficients. Keep the variables. Simplify each polynomial Ex 1: - 6x + 5y – 3x + y – 8 Ex 2: -2x – 8y + 5x – 4y = -6x – 3x + 5y + y – 8 = - 2x + 5x - 8y – 4y = - 9x + 6y – 8 = 3x - 12y EX 3: 5a – 2b + c – 5b + 4b Ex 4: 4x2 - 6x + 3x – 4x2 + 7x2 + 1 - 5 = 5a – 2b + 4b + c = 4x2 – 4x2 + 7x2 – 6x + 3x + 1 – 5 = 5a + 3b + c = 7x2 - 3x - 4
- 20. LET’S PRACTICE!- SIMPLIFY EACH EXPRESSION • -5x + 4x – 7 – x – 2 = • 3m – 8m – 5d – 2d – 4m = • - 8 – b – 5d – 2d – 4m = • 3y – 2y + 9 – 5y – 4 = • - 23g – 12 + 8d – 9g + 3d =