How do you factor the perfect square trinomial? How do you factor the sum and
difference of two cubes?
a2-b2=(a-b)*(a+b). You can check it by simply multiplying the first parentheses and the second ones. You will end up with a2-ab+ab-b2=a2-b2.
If a trinomial is a perfect square, it shall be of the form a2±2ab+b2. Then it is factored as (a±b)*(a±b).
As for the sum and difference of two cubes, the formulas are as follows:
Again, you can check it by multiplication.