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More stuff from my textbook that I'm not quite understanding, help is appreciated. I'll be trying to figure it out and updating my question as I wait for answers.

I understand how $3k^2+3k$ factors to become $3(k^2+k)$, but what's happening to the $+1$ tacked on at the end?

EDIT: I see about the $+1$, since we're subtracting $k+1$, that means that the $+1$ is being removed from our left side equation.

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The +1 from the first term gets canceled by the one from the second term – Jean-Sébastien Oct 30 '12 at 23:48
You have $1-1=0$. – Julian Kuelshammer Oct 30 '12 at 23:48
Yeah I just saw that, I don't know why my brain misses this simple stuff. It's frustrating. – Unknown Oct 30 '12 at 23:48
up vote 4 down vote accepted

Simplify both sides and check if they are equal

$$\begin{align*}(k^3 + 3k^2 + 3k + 1)−(k + 1)&=(k^3−k)+3(k^2 + k)\\\\ k^3 + 3k^2 +\color{red}{3k}+\color{blue}{1}-\color{red}{k}-\color{blue}{1}&=k^3\color{red}{-k}+3k^2+\color{red}{3k}\\\\ k^3 + 3k^2 + 2k&=k^3+3k^2+2k \end{align*}$$

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