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binomial expansion

sammy3000

find the coefficient of the term x^3 in the expansion of(2+3x)^3(5-x)^3.

Reply 1

ghostwalker

sammy3000

find the coefficient of the term x^3 in the expansion of(2+3x)^3(5-x)^3.

What have you done so far?

Reply 2

username165864

First expand the first and second terms using Binomial expansion. And as you are multiplying the two together, any terms higher than x^3 post-multiplication can be discarded (and in fact any constants, x, and x^2 terms can also be ignored). Add together the coefficients of the x^3 terms and you have your answer!

Reply 3

simontinsley

(2+3x)^3(5-x)^3

(2+3x)^3 = 2^3 + 3*2^2*3x + 3*2*3^2x^2 + 3^3 x^3 = 8 + 36x + 54x^2 + 27x^3

(5-x)^3 = 5^3 + 3*5^2*(-1)x + 3*5*(-1)^2x^2 + (-1)^3 x^3 = 125 - 75x + 15x^2 - x^3

x^3

can come from:

x^3 * integer

x^2*x

.

So

x^3

coefficient =

8*(-1)+ 36*15 + 54*(-75) + 125*27 = -143

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