# 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 a(b -

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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 a(b - c) = ab - ac Example #1 5(x + 7) 5 x + 5 7 5x + 35

Example using the distributive property

Another Example

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? 1.3(x + y + z) = 3x + 3y + 3z 2.(a + b) c = ac + bc 3.5(2 + 3x) = 10 + 3x 4.6(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 2x 2

The coefficient is the numerical part of the term. Examples 1) 4a 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) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesnt matter. 3) x 3 y, xy 3 No, the exponents are on different variables.

Combining Like Terms

Which of the following is the simplified form of -4x + 7x ? 1.-4 2.3x 3.-3x 4.4 Answer Now

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

12a 2) 6.1y - 3.2y 2.9y 3) 4x 2 y + x 2 y 5x 2 y 4) 3m 2 n + 10mn 2 + 7m 2 n - 4mn 2 10m 2 n + 6mn 2 Simplify Expressions 1) 5a + 7a

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

Which of the following is the simplified form of 5x - 4 - 7x + 14 ? Answer Now 1.-12x + 10 2.-2x + 10 3.2x - 18 4.12x – 18

If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle? Answer Now 1.4x - 2 2.4x + 2 3.5x - 2 4.5x - 7

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

Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? Answer Now 1.-36 2.3a - 36 3.8a - 36 4.8a + 36

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