Factor $(y^{3} – 125)$

factoringpolynomials

I know this is a really elementary problem, but I can't seem to figure it out.
How do you factor: $(y^{3}-125)$?
The answer I got is $(y+5)(y^{2}-5y-25)$ but something about the signs just doesn't work.
How should this be factored?

Best Answer

This is just the difference of cubes.
The way to factor the difference of cubes is: $$(a^{3}-b^{3}) = (a-b)(a^{2}+ab+b^{2})$$.
In this case, your problem is really asking: $(y^{3}-5^{3})$. $y$ is $a$ and 5 is $b$. When you plug it all in, you get $(y-5)(y^{2}+5y+25)$. Your answer is almost right, but the signs are mixed up.

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