Chapter 1 Section 4 Distributive Property

Symbols: For any numbers a, b, c, a(b + c) = ab + ac and a(b - c) = ab – ac. Numbers: 2(5 + 3) = (2 ∙ 5) + (2 ∙ 3) 2(5 - 3) = (2 ∙ 5) - (2 ∙ 3)

Example 1 Simplify each expression. 3(x + 7) 3(x + 7) = (3 ∙ x) + (3 ∙ 7) = 3x + 21 Distributive Property Substitution Property

Example 1 Simplify each expression. 5(2n + 8) 5(2n + 8) = (5 ∙ 2n) + (5 ∙ 8) = 10n + 40 Distributive Property Substitution Property

Your Turn Simplify each expression. 6(a + b) 6a + 6b

Your Turn Simplify each expression. (1 + 3t) t

Vocabulary Term- A term is a number, variable, or product of numbers and variables. Coefficient- The numerical part of a term that contains a variable is called the coefficient. Like Terms- Like Terms are terms that contain the same variables, such as 2a and 5a or 7xy and 3xy. Equivalent Expressions- The expression 2n + 7n and 9n are equivalent because their values are the same. Simplest Form- You can write an algebraic expression in simplest form by writing an equivalent expression having no like terms and no parentheses.

Example 3 Simplify each expression. 4x + 9x 13x You can add like terms together because they have the same variable.

Example 4 Simplify each expression. a + 7b + 3a – 2b (a + 3a) + (7b – 2b) 4a + 5b

Your Turn Simplify each expression. 5st + 2st 7st

Your Turn Simplify each expression. 6 + y + 3z + 4y 6 + 5y + 3z

Example 5 Write an equation representing the area A of a soccer field given its width w and length l as shown below. Then simplify the expression and find the area if w is 54 yards and l is 60 yards. A = w(l + l) = 54 ( ) = 54 (120) = 6480 w ll

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