Section 2 6 The Distributive Property The Distributive

Section 2. 6 The Distributive Property

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.

Which of the following is the simplified form of -4 x + 7 x ? 1. 2. 3. 4. -4 3 x -3 x 4 Answer Now

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

Simplify 1) 5 a + 7 a 12 a 2) 6. 1 y - 3. 2 y 2. 9 y 3) 4 x 2 y + x 2 y 5 x 2 y 4) 3 m 2 n + 10 mn 2 + 7 m 2 n - 4 mn 2 10 m 2 n + 6 mn 2

5) 13 a + 8 a + 6 b 21 a + 6 b 6) 4 d + 6 a 2 - d + 12 a 2 18 a 2 + 3 d 7) y

Which of the following is the simplified form of 5 x - 4 - 7 x + 14 ? 1. 2. 3. 4. -12 x + 10 -2 x + 10 2 x - 18 12 x – 18 Answer Now

If a triangle has sides 3 x - 2, 5 - x and 2 x - 5, what is the perimeter of the triangle? 1. 2. 3. 4. 4 x - 2 4 x + 2 5 x - 7 Answer Now

Which figure below models the simplification of - 4 x - 5 + 7 x + 7 using these tiles? 1. 2. 3. 4. Answer Now

Bonus! Which of the following is the simplified form of a + 3 a - 4(9 - a) ? 1. 2. 3. 4. -36 3 a - 36 8 a + 36 Answer Now