# How to find the coeficient of x^3 in the expansion (1-0.5x)^2(1+2x)^7?

Would much appreciate any help. I have an exam in 2 days.

Thank you

Posted Mon 14th May, 2012 @ 18:25 by divya.k

x^3 can be made when X^2  * X or when X^3 times any number

so binomially expand the first part to give (1-X + 0.25X^2)

expand the second part to to the X^3 term.   this gives (1+ 14X + 84X^2 +280X^3 ...)

multiply the relevant terms together. so 1*280X^3 +  X * 84X^2 + 0.25X^2 * 14X

this gives 367.5X^3

so the coefficient is 367.5

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Answered Mon 14th May, 2012 @ 19:48 by Pui Pui

is there something missing in the question?.. in-between the squared and the (1+2x)^7 ?

Answered Mon 14th May, 2012 @ 19:19 by Lalloo19

Thank you so much Pui Pui, your method helped so much, and you made it really simple.

The answer you got was incorrect, probably a small mistake but I used your method to get the correct answer: 199.5

Really good explanation.

Thank you again for your help, I really appreciate it :D x

Answered Mon 14th May, 2012 @ 20:31 by divya.k
Edited by divya.k on Mon 14th May, 2012 @ 20:38