Difference of Perfect Squares
A Difference of Perfect Squares is a special class of binomial where:
1. Coefficients are perfect squares.
2. Constants are perfect squares.
3. Powers on variable terms are even.
16x^{2}-81 is a perfect square
8x^{2}-81 is not a perfect square, because 8 is not a perfect square
How to factor a binomial that is the difference of perfect squares?
Algebra rule:
To factors the difference of two perfect squares, use the following pattern:
a^{2}-b^{2}=(a+b)(a-b)
The sum of two perfect squares, a^{2}+b^{2}, is nonfactorable over the integers.
Factor x
^{2}-16
x^{2}-16=(x-4)(x+4)
Factor x
^{6}-4y
^{2}
x^{6}-4y^{2}=(x^{3}-2y)(x^{3}+2y)