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

Question

Mathematics

Shaffer

21 January, 18:22

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

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Brendon Durham · Answer 1

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