The Distributive Property and Terms A term is

The Distributive Property and Terms

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

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

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