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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Chapter 8.6

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems Students will know how to multiply a polynomial by a monomial using distribution and the laws of exponents.

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Example 1: Find -3x 2 (4x 2 + 6x – 8) Use the distributive property to multiply the monomial into the parenthesis. -3x 2 (4x 2 ) + (-3x 2 )(6x) – (-3x 2 )(8)

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Remember when multiplying monomials you multiply the numbers and letters separately. When multiplying the variables you add the exponents. -3x 2 (4x 2 ) + (-3x 2 )(6x) – (-3x 2 )(8) -12x 4 – 18x 3 + 24x 2

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2x(3x 2 + 2x – 5) 2.5x 2 (6x 3 – 3x 2 + 2) 3.8xy(2x 3 y 2 + 3x – 4y)

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2x(3x 2 + 2x – 5) 2.5x 2 (6x 3 – 3x 2 + 2) 3.8xy(2x 3 y 2 + 3x – 4y) 6x 3 + 4x 2 – 10x 30x 5 – 15x 4 + 10x 2 16x 2 y 3 + 24x 2 y – 32xy 2

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Example 2: Simplify: Do the parenthesis first and use the distributive property to simplify. Remember, the second parenthesis is being multiplied by a negative x value.

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Combine like terms

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2(3x 2 + 2x) + x(4x – 3) 2.4x(2x + 5) – 2(4x 2 + 10x – 4) 3.2x(3x – 4) – 3x(4x 2 + 3x – 2)

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2(3x 2 + 2x) + x(4x – 3) 2.4x(2x + 5) – 2(4x 2 + 10x – 4) 3.2x(3x – 4) – 3x(4x 2 + 3x – 2) 10x 2 + x 8 -12x 3 – 3x 2 – 2x

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Example 3: Solve: Distribute first on both sides Make sure you only distribute to inside the parenthesis

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Combine like terms on each side of the equals sign Now we have to get all the x’s on one side of the equals I usually move the smaller one, so add 6x to both sides

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL Add 8 to both sides Divide by 15

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2(2x + 3) = 3(x + 7) 2.3(2x – 2) + 2x = 12 + 2(2x – 5) 3.2x(3x + 4) + 2 = -13 – 3(-2x 2 – x)

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2(2x + 3) = 3(x + 7) 2.3(2x – 2) + 2x = 12 + 2(2x – 5) 3.2x(3x + 4) + 2 = -13 – 3(-2x 2 – x) x = 15 x = 2 x = -3

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2x 2 (3x 2 + 5x – 4) 2.2(x + 3) – 3(2x + 4) 3.2x 2 (3x – 2) + 4x(5x 2 – 3) 4.4(3x – 2) – 2x = 14 + 2(x + 5) 5.3x(-2x + 3) + 6 = -9 – 2(3x 2 – 2x)

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M ULTIPLYING A P OLYNOMIAL BY A M ONOMIAL 1.2x 2 (3x 2 + 5x – 4) 2.2(x + 3) – 3(2x + 4) 3.2x 2 (3x – 2) + 4x(5x 2 – 3) 4.4(3x – 2) – 2x = 14 + 2(x + 5) 5.3x(-2x + 3) + 6 = -9 – 2(3x 2 – 2x) 6x 4 + 10x 3 – 8x 2 -4x – 6 26x 3 – 4x 2 – 12x x = 4 x = -3

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