$x^2 * (x+1)^2 = (x^2+x)^2$|| I do not understand this

Question

$$x^4(x+1)^4(2x+1)$$ I was solving this question (I had integrate it) but I did not know how to solve it! So I saw the solution and it says

$$x^4(x+1)^4 = (x^2+x)^4$$

and I do not get how that works? Can someone prove it, please?

Answer 1

$$x^4(x+1)^4 = \left(x(x+1)\right)^4=(x^2+x)^4$$

Answer 2

$$\int x^4(x+1)^4(2x+1){\rm d}x=\int (x^2+x)^4{\rm d}(x^2+x)=\frac{1}{5}(x^2+x)^5+C.$$