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Published byPhoebe Whitehead Modified over 8 years ago

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Multiplying Polynomials

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To multiply exponential forms that have the same base, we can add the exponents and keep the same base.

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Multiply the Coefficients Add the Exponents of the like variables

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4y 5 × 6y 3 - 5p 3 × 6p - 9g 7 × 7g 2 - 3x 3 × 4x × -2x 2

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4y 5 × 6y 3 (4)(6)(y 5+3 ) 24y 8 - 5p 3 × 6p (-5)(6)(p 3+1 ) -30p 4 - 9g 7 × 7g 2 (-9)(7)(g 7+2 ) -63g 9 - 3x 3 × 4x × -2x 2 (-3)(4)(-2)(x 3+1+2 ) 24x 6

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To simplify an exponential form raised to a power, we can multiply the exponents and keep the same base Evaluate the coefficient raised to that power. Multiply each variable’s exponent by that power.

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OR Trying Another Example

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To Multiply a polynomial by a monomial, use the distributive property to multiply each term in the polynomial by the monomial. 2(3 + 4) = (2)(3) + (2)(4) X(3 + 4) = (X)(3) + (X)(4)

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Combine each term in the second polynomial by each term in the first polynomial Combine like terms

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F First O Outside(x + 3)(x + 2) I Inside L Last

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Conjugates are binomials that differ only in the sign that separating the terms. The conjugate of (x + 7) = (x – 7)

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(x + 7)(x – 7) = x 2 - 7 2

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(t + 3)(4t -1) (n – 6)(7n – 3) (y + 8)(y – 8) (x + 4)(2x 2 + 5x – 3) 3x 2 (2x – 3)(x + 4)

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