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Math Help - Binomial theorem question check #2

  1. #1
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    Binomial theorem question check #2

    hey guys, just need to check if my working out and solution is correct.

    Find the coefficient of x^5 in (3 - 4x)(2x+3)^7

    My solution

    So I started off by separating both brackets into 2 separate equations.

    1. 3(2x+3)^7
    2. -4x(2x+3)^7

    Now I find the coefficient of x^5 in equation 1 and I find the coefficient of x^4 in equation 2.

    So now:

    1. 3 \binom{7}{5} (3)^2 (2)^5 = 3 \times 21 \times 9 \times 32

    2. -4 \binom{7}{4} (3)^3 (2)^4 = -4 \times 35 \times 27 \times 16

    So now adding both up:

    Solution: 3 \times 21 \times 9 \times 32 - 4 \times 35 \times 27 \times 16
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  2. #2
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    Hello jvignacio
    Quote Originally Posted by jvignacio View Post
    hey guys, just need to check if my working out and solution is correct.

    Find the coefficient of x^5 in (3 - 4x)(2x+3)^7

    My solution

    So I started off by separating both brackets into 2 separate equations.

    1. 3(2x+3)^7
    2. -4x(2x+3)^7

    Now I find the coefficient of x^5 in equation 1 and I find the coefficient of x^4 in equation 2.

    So now:

    1. 3 \binom{7}{5} (3)^2 (2)^5 = 3 \times 21 \times 9 \times 32

    2. -4 \binom{7}{4} (3)^3 (2)^4 = -4 \times 35 \times 27 \times 16

    So now adding both up:

    Solution: 3 \times 21 \times 9 \times 32 - 4 \times 35 \times 27 \times 16
    Looks good to me!

    Grandad
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