<s>[INST] Does $4(x^3+2x^2+x)^3(3x^2+4x+1) = 4x^3(3x+1)(x+1)^7$? Please provide proof
The answer in the back of the book is different to both my calculations and also the online calculator I crosschecked my answer with...

The Question:
"Differentiate with respect to $x$:"
$
(x^3+2x^2+x)^4
$
My Answer: $4(x^3+2x^2+x)^3(3x^2+4x+1)$
The Book's Answer: $4x^3(3x+1)(x+1)^7$
 [/INST] Note that $(x^3+2x^2+x)=x(x^2+2x+1)=x(x+1)^2$.
Also, $3x^2+4x+1=(x+1)(3x+1)$
Apply those factorizations to your answer, and collect like factors together; you should get the book's answer.
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