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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 − ( cd)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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