Expand (3 – 2x)6. What is the coefficient of the sixth term?

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Expand (3 – 2x)6. What is the coefficient of the sixth term?

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    2021-11-23T22:24:49+00:00

    To expand (3 – 2x)^6 use the binomial theorem:

    (x + y)^ n = C(n,0) x^ny^0 + C(n,1)x^(n-1) y + C(n,2)x^(n-2) y^2 + …+ C(n,n+1)xy^(n-1) + C(n,n)x^0y^n

    So, for x = 3, y = -2x , and n = 6 you get:

    (3 – 2x) ^6 = C(6,0)(3)^6 + C(6,1)(3)^5 (-2x) + C(6,2) (3)^4 (-2x)^3 + C(6,3) (3^3) (-2x)^4 + C(6,4)(3)^2 (-2x)^4 + C(6,5) (3) (-2x)^5 + C(6,6) (-2x)^6

    So, the sixth term is C(6,5)(3)(-2x)^5 =  6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = – 6*3*32 = – 576 x^5.

    The coefficient of that term is – 576.

    Answer: – 576

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