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What is the product of the polynomials (4x^3+8x)(x^2-1) A. 4x^5+8x^2-8x B.4x^5+4x^3+32 C.4x^5-4x^3+8x^2-8x D.4x^5+4x^3-8x

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rules (a+b)(c+d)=ac+ad+bc+bd and a^m x a^n = a^(m+n)

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To multiply polynomials, take every term from one polynomial and multiply it by every term in the other, so a simple example: (a + b)(x + y) = ax + ay + bx + by you can see that a was multiplied by both terms (x and y) as was b, then the results are all added together. So your problem: (4x³ + 8x)(x² - 1) same thing, just being sure to keep track of exponents. 4x³ gets multiplied by both terms in the other, as does 8x, to give: 4x⁵ - 4x³ + 8x³ - 8x Now we can combine like terms to simplify: 4x⁵ + 4x³ - 8x Option D is your answer.

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obviously D)

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4x^5-4x^3+8x^3-8x = 4x^5+4x^3-8x Answer D


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