<s>[INST] Find $a$, $b$, $c$, $d$ such that $(ax+b)^2(x+c) = 4x^3 + dx^2 + 55x - 100$ How would I find $a$, $b$, $c$, and $d$ in :
$$(ax+b)^2(x+c) = 4x^3 + dx^2 + 55x - 100$$
I have already worked out that $a=2$, but I may be wrong. I am not sure how to find the values of the other letters. 
Thanks in advance!
 [/INST] Hint: $$(ax+b)^2(x+c)={a}^{2}c{x}^{2}+{a}^{2}{x}^{3}+2\,abcx+2\,ab{x}^{2}+{b}^{2}c+x{b}^{2}=a^2x^3+x^2(a^2c+2ab)+x(2abc+b^2)+b^2c$$
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