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.
