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Binomial expansions

Hello. i need some help working out this problem:

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

is anyone able to help??? will be appreciated!

thanks

Reply 1

username9816

slop8

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

(2+3x)^3(5-x)^3 = [8 + 3(2^2)(3x) + 3(2)(3x)^2 + 1(1)(3x)^3][125 + 3(5^2)(-x) + 3(5)(-x)^2 + 1(1)(-x)^3] = [8 + 36x + 54x^2 + 27x^3][125 - 75x + 15x^2 - x^3]

Hence:
Co-efficient (x^3 term) = 8(-1) + 36(15) + 54(-75) + 27(125) = -143

Reply 2

slop8

Nima

hello and thanks for the reply but im sorry to say thats not the correct answer....i know its somewhere near -143 but just dont know how to work it out.

Reply 3

BCHL85

Wow
x^3 = x^3 = x.x^2 = x^2.x
So (2+3x)^3 = 8 + 12x + 54x^2 + 27x^3
(5-x)^3 = -x^3 + 15x- 75x + 125
You need coefficient of x^3. It's
k = -8 + 12*15 -54*75 + 27*125
Note: Just multiply coeffiecient of 2 columns.