11.5 Factoring Perfect Square Trinomials and Difference of Squares
A trinomial that is the square of a binomial is called a perfect square trinomial.
( + ) =
( − ) =
+2
Examples: Factor each trinomial completely.
+
1.
2.
−6 +9
−2
+
A. ( + 3)
+ 8 + 16
B. ( + 3)( − 3)
C. ( − 3)
D. ( − 6)( + 6)
3.
− 20 + 100
4. 4
5.
+ 16
6. 25
+ 64
− 12 + 9
− 64
A. (5 + 8)(5 − 8)
B. (5 − 8)
C. (5 + 8)
D. prime
Difference of Squares
A binomial is the difference of two squares if both terms are squares and the signs of the terms are
different.
( − )( + ) =
−
Examples: Factor the difference of squares.
7.
− 81
9. 25
8. 4 −
− 36
11. 16
− 256
13. 125
− 80
10.
+1
12. 121 −
14. Factor by grouping: 5
−9 −2