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 5x + 35

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

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

A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x2

the numerical part of the term. The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y2 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) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x3y, xy3 No, the exponents are on different variables.

Which of the following is the simplified form of -4x + 7x ? Answer Now

5a and a are like terms and are like terms The above expression simplifies to:

Simplify 1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2

5) 13a + 8a + 6b 21a + 6b 6) 4d + 6a2 - d + 12a2 18a2 + 3d 7) y

Which of the following is the simplified form of 5x - 4 - 7x + 14 ? Answer Now