Recall that the product of conjugates produces a pattern called a difference of squares.
Example 1
Factor x ^{2} – 16.
This polynomial results from the subtraction of two values that are each the square of some expression.
Example 2
Factor 25 x ^{2} y ^{2} – 36 z ^{2}.
Example 3
Factor ( a + b) ^{2} – ( c – d) ^{2}.
Example 4
Factor y ^{2} + 9.
Even though y ^{2} and 9 are square numbers, the expression y ^{2} + 9 is not a difference of squares and is not factorable.
Many polynomials require more than one method of factoring to be completely factored into a product of polynomials. Because of this, a sequence of factoring methods must be used.

First, try to factor by using the GCF.

Second, try to factor by using the difference of squares.
Example 5
Factor 9 x ^{2} – 36.
Example 6
Factor 8( x + y) ^{2} – 18.
Note: 4( x + y) ^{2} = [2( x + y)] ^{2} and 9 = 3 ^{2}.