How do you factor the difference of two squares?

Question

How do you factor the perfect square trinomial? How do you factor the sum and
difference of two cubes?

Answer 1

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:

a³+b³=(a+b)*(a²-ab+b²).

a³-b³=(a-b)*(a²+ab+b²).

Again, you can check it by multiplication.