1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental Mathematics Section 12.4: Special Factoring Techniques

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Factoring the Difference of Two Squares Factor completely.

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Sum of Two Squares The sum of two squares is an expression of the form x 2 + a 2 and is not factorable. For example, x 2 + 36 is the sum of two squares and is not factorable. There are no factors with integer coefficients whose product is x 2 + 36. To understand this situation, write x 2 + 36 = x 2 + 0x +36 and note that there are no factors of +36 that will add to 0.

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Factoring Perfect Square Trinomials Factor completely.

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Factoring Perfect Square Trinomials

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Sums and Differences of Two Cubes o Factor out the GCF first o The exponents on the variables must be multiples of 3 OR

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Factoring Sums and Differences of Two Cubes Factor completely. x 3  8

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Factoring Sums and Differences of Two Cubes

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Factoring Sums and Differences of Two Cubes