1. Example 2 Factor the polynomial. 12n n2 a. – 36 + = ( ) 2 n2 – 62 + 6
Factor perfect square trinomials
Factor the polynomial.
12n n2 a. – 36 +
Write as = ( ) 2 n2 – 62 + 6 n •
2ab a2 b2 ( )2 6 n –
Perfect square trinomial pattern =
12x
9x2 b. – 4 +
Write as = ( ) 2 – 22 + 3x •
2ab a2 b2 )2 ( )2 2 3x –
Perfect square trinomial pattern =
4st
4s2 c. t2 +
Write as = ( ) 2 + t2 t 2s •
2ab a2 b2 )2 ( )2 t 2s +
Perfect square trinomial pattern =

2. [ ] Example 3 What is the factored form of ? 36xy 3x2 108y2 + – 3x 6y
Multiple Choice Practice
Example 3
What is the factored form of ?
36xy
3x2
108y2 + – 3x 6y – ( )2 x 6y + ( )2 3 – 3x 6y – ( )2 x 6y ( )2 3 –
SOLUTION
36xy
3x2
108y2 + –
12xy x2
36y2 3 ( ) =
Factor out ( ) 2 – + 6y x • x2 )2 [ ] 3 =
Write as
12xy
36y2
2ab a2 b2 2

3. Example 3 x 6y ( )2 3 – = ANSWER The correct answer is D.
Multiple Choice Practice
Example 3 x 6y ( )2 3 – =
Perfect square trinomial pattern
ANSWER
The correct answer is D. 3

4. Guided Practice Factor the polynomial. 2. h2 + 4h + 4 ANSWER ( )2 2 +
for Examples 2 and 3
Factor the polynomial. 2. h2 + 4h + 4
ANSWER ( )2 2 + h 3.
20y
2y2 – 50 +
ANSWER ( )2 5 y – 2 4.
12z
18z2 2 +
ANSWER ( )2 1 + 3z 2 5.
24t
4t2 – 36 +
ANSWER ( )2 3 t – 4 6.
6xy
3x2
3y2 +
ANSWER ( )2 y x + 3

5. Guided Practice Factor the polynomial. 7. 12xy x2 36y2 + ANSWER ( )2
for Examples 2 and 3
Factor the polynomial. 7.
12xy x2
36y2 +
ANSWER ( )2 6y x +