The Distributive Property 1-5

Objective: Students will use the Distributive Property to evaluate expressions and to simplify expressions.

S. Calahan2008

The Distributive Property

• For any numbers a, b, and c,a(b + c) = ab + ac or a(b – c) = ab

– ac

Example: 3(2 + 5) = 3 • 2 + 3 • 5 3(7) = 6 + 15 21 = 21

Algebraic Expressions: Distribute

5(g – 9)= 5 • g – 5 • 9= 5g - 45

3(2x2 + 4x – 1)

3(2x2) + 3(4x) -3(1)= 6x2 + 12x - 3

vocabulary

•Term – a number, a variable, or a product or quotient of numbers and variables.

•Examples: y, p3, 4a, 5gh• 2x2 + 6x + 5 has three terms

Like Terms•Terms that contain the same variables with the same powers.

•Example: 3a2 + 5a2 + 2a•3a2 and 5a2 are like terms.

Coefficient

•The numerical factor of a term.

•Example: 17xy the coefficient is the 17.

Equivalent expressions

•Equal the same number.•Example: 5n + 7n = 12n•Simplest form – having no like terms or parentheses.

Simplify the expressions.

•17a + 21a = 38a•12b2 – 8b2 + 6b = 4b2 + 6b

14a2 + 13b2 + 27

•This is already simplified because there are not any like terms.