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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

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Example using the distributive property

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Another Example

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

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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

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

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

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

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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.

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Combining Like Terms

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

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

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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

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

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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

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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

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

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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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Columbus State Community College

Columbus State Community College

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