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Warm-up: Simplify. 1.6 (3x - 5) = 18x - 30 2.4 (2x + 10) = 8x + 40 3.9y - 3y = 6y 4.7a + 4b + 3a - 2b = 10a + 2b 5.4 (3x + 2) + 2 (x + 3) = 14x + 14

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Multiplying Polynomials Objective: Multiply two monomials Multiply a monomial by a polynomial

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Why are the following not monomials? x + y addition division 2 - 3a subtraction

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Multiplying Monomials When multiplying monomials, you ADD the exponents. 1) x 2 x 4 x 2+4 x6x6 2) 2a 2 y 3 3a 3 y 4 6a 5 y 7

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Simplify m 3 (m 4 )(m) 1.m 7 2.m 8 3.m 12 4.m 13

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Power of a Power When you have an exponent with an exponent, you multiply those exponents. 1) (x 2 ) 3 x 2 3 x6x6 2) (y 3 ) 4 y 12

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Simplify (p 2 ) 4 1.p 2 2.p 4 3.p 8 4.p 16

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Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. 1) (2a) 3 23a323a3 8a 3 2) (3x) 2 9x 2

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Simplify (4r) 3 1.12r 3 2.12r 4 3.64r 3 4.64r 4

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Power of a Monomial This is a combination of all of the other rules. 1) (x 3 y 2 ) 4 x 3 4 y 2 4 x 12 y 8 2) (4x 4 y 3 ) 3 64x 12 y 9

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Simplify (3a 2 b 3 ) 4 1.12a 8 b 12 2.81a 6 b 7 3.81a 16 b 81 4.81a 8 b 12

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add the exponents! 1) Simplify: 5(7n - 2) Use the distributive property. 5 7n 35n - 10 Review: When multiplying variables, - 5 2

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2) Simplify: 6a 2 + 9a 3) Simplify: 6rs(r 2 s - 3) 6rs r 2 s 6r 3 s 2 - 18rs - 6rs 3

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4) Simplify: 4t 2 (3t 2 + 2t - 5) 12t 4 5) Simplify: - 4m 3 (-3m - 6n + 4p) 12m 4 + 8t 3 - 20t 2 + 24m 3 n- 16m 3 p

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6) Simplify: (27x 2 - 6x + 12) 16x 3 - 28x 2 + 4x Fooled ya, didn’t I?!? Ha! Ha! Here’s the real answer! -9x 3 + 2x 2 - 4x

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Simplify 4y(3y 2 – 1) 1.7y 2 – 1 2.12y 2 – 1 3.12y 3 – 1 4.12y 3 – 4y

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Simplify -3x 2 y 3 (y 2 – x 2 + 2xy) 1.-3x 2 y 5 + 3x 4 y 3 – 6x 3 y 4 2.-3x 2 y 6 + 3x 4 y 3 – 6x 2 y 3 3.-3x 2 y 5 + 3x 4 y 3 – 6x 2 y 3 4.3x 2 y 5 – 3x 4 y 3 + 6x 3 y 4

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