Difference of Squares

Recall that the product of conjugates produces a pattern called a difference of squares.

Example 1: Factor x² − 16

This polynomial results from the subtraction of two values that are each the square of some expression

Example 2: Factor 25 x²y² − 36 z²

Example 3: Factor ( a + b)² − ( c − d)².

Example 4: Factor y² + 9.

Even though y² and 9 are square numbers, the expression y² + 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 x² − 36.

Example 6: Factor 8( x + y)² − 18.

Note: 4( x + y)² = [2( x + y)]² and 9 = 3².

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