<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] $4(x^3+2x^2+x)^3 . (3x^2+4x+1)$
$4x^3 (x^2+2x+1)^3 (3x^2+4x+1)$
$4x^3 (x+1)^6      (3x^2+4x+1)$
$4x^3 (x+1)^6      (3x+1)(x+1)$
$4x^3 (x+1)^7 (3x+1)$
So the book resolved your result in more factors.
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