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The coefficient of x in the binomial expansion of (2-4x) ^q , where q is a positive integer, is -32q. Find the value of q?

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Dr. Badi M

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(2-4x)^q = 2^q (1-2x)^q Binomial expansion (1+x)^n = (1+nx+......etc.) So above becomes 2^q (1 -2qx+...) Coefficient of x is -2^(q+1)q = -32q Then (-q) cancels from both sides and you get 2^(q+1) = 32 Same as 2^(q+1) = 2^5 So q+1 = 5 Gives you q= 4

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