Objectives The student will be able to use

Objectives • The student will be able to use the distributive property to simplify expressions. • Understand what are terms, like terms, coefficients and how they can be combined

The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac and (b + c) a = ba + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5 • x+5 • 7 5 x + 35

Example #2 3(m - 4) 3 • m-3 • 4 3 m - 12 Example #3 -2(y + 3) -2 • y + (-2) • 3 -2 y + (-6) -2 y - 6

Which statement demonstrates the distributive property incorrectly? 1. 2. 3. 4. 3(x + y + z) = 3 x + 3 y + 3 z (a + b) c = ac + bc 5(2 + 3 x) = 10 + 3 x 6(3 k - 4) = 18 k - 24 Answer Now

A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2 x 2

The coefficient is the numerical part of the term. Examples 1) 4 a 4 2) y 2 1 3)

Like Terms are terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

Are these like terms? 1) 13 k, 22 k Yes, the variables are the same. 2) 5 ab, 4 ba Yes, the order of the variables doesn’t matter. 3) x 3 y, xy 3 No, the exponents are on different variables.