1. Factoring Perfect-Square Trinomials and Differences of Squares
5.4
Recognizing Perfect-Square Trinomials
Factoring Perfect-Square Trinomials
Recognizing Differences of Squares
Factoring Differences of Squares
Factoring Completely

2. Recognizing Perfect-Square Trinomials
A trinomial that is the square of a binomial is called a perfect-square trinomial. A2 + 2AB + B2 = (A + B)2; A2 – 2AB + B2 = (A – B)2

3. Determine whether each of the following is a perfect-square trinomial
Determine whether each of the following is a perfect-square trinomial. a) x2 + 8x + 16 b) t2  9t  36 c) 25x2 + 4  20x Solution

4. Factoring a Perfect-Square Trinomial
A2 + 2AB + B2 = (A + B)2;
A2 – 2AB + B2 = (A – B)2

5. Factor: a) x2 + 8x + 16 b) 25x2  20x + 4
Solution

6. Sage and Scribe
Factor: 16a2  24ab + 9b2
Factor:
12a3 108a a

7. Recognizing Differences of Squares
An expression, like 25x2  36, that can be written in the form A2  B2 is called a difference of squares.

8. Determine whether each of the following is a difference of squares
Determine whether each of the following is a difference of squares. a) 16x2  25 b) 36  y5 c) x Solution

9. Factoring a Difference of Squares
A2 – B2 = (A + B)(A – B).

10. Factor: a) x2  9 b) y2  16w2
Solution

11. Factor 5x4  125.
Solution

12. Sage and Scribe
25  36a12 b) 98x2  8x8

13. Tips for Factoring
1. Always look first for a common factor! If there is one, factor it out.
2. Be alert for perfect-square trinomials and for binomials that are differences of squares. Once recognized, they can be factored without trial and error.
3. Always factor completely.
4. Check by multiplying.