Studying for a big test trying to do the derivative of $x(x+2)^3$.
I did the product rule and got $3x(x+2)^2 + (x+2)^3$. Pretty standard stuff.
I got half credit and was told to simplify it like this:
How in the world do you get from my answer (second line) to the third line? It doesn't even make algebraic sense. I will be going to office hours tomorrow, but if this is my mistake I don't want to bother her. I just don't see it...
Let $(x+2)=a$ and $3x=b$.
Thus, $3x(x+2)^2+(x+2)^3=ba^2+a^3=a^2(b+a)$ Then, back substitute to verify that our expressions are equal.
Overall, we factored out a common factor of $(x+2)^2$ from each term in the expression.