Question

Factor completely p^4-81

Answer 1

$(p^{2}-9)(p^{2}+9) = p^4+9p^{2}-9p^{2}-81 = p^{4}-81$

The left side of the equation is what you get if you apply the "foil" method to the middle. This is the first step. Now the left-hand side is only partially factored, because you can still factor one of the remaining terms. Notice that one of the terms on the left has a similar form to that of the original question p^4-81. You can apply the same method I did to that term and then you will have fully factored p^4-81. You should have 3 factors in the end. Hope this helps!