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 =

[ ] 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

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

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

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 +