How do you factor the perfect square trinomial? How do you factor the sum and

difference of two cubes?

a^{2}-b^{2}=(a-b)*(a+b). You can check it by simply multiplying the first parentheses and the second ones. You will end up with a^{2}-ab+ab-b^{2}=a^{2}-b^{2}.

If a trinomial is a perfect square, it shall be of the form a^{2}±2ab+b^{2}. Then it is factored as (a±b)*(a±b).

As for the sum and difference of two cubes, the formulas are as follows:

a^{3}+b^{3}=(a+b)*(a^{2}-ab+b^{2}).^{
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a^{3}-b^{3}=(a-b)*(a^{2}+ab+b^{2}).

Again, you can check it by multiplication.