Warmups – factor.

1) 2xy3 – 6x2y

2) x2 – 12x + 36

3) 4y2 + 36y + 81

4) 4ax – 6bx + 6ay – 9by

10-5 Perfect Square Trinomials

Objective: To identify and factor perfect square trinomials.

Standard 11.0

Remember…

So….

2( )a b 2 22a ab b

2 22a ab b 2( )a b

Recognizing a Perfect Square Trinomial

4x2 + 36xy + 81y2

1st term is a perfect square 3rd term is a perfect square (and positive) 2nd = 2•√1st •√3rd , can be positive or negative Then…

Example

x2 – 12x + 36

(x – 6)2

2(2 )x2(9 )y

2(2 )(9 )x y2(2 9 )x y

TOO: IS IT A PERFECT SQUARE TRINOMIAL?

1) x2 + 8x + 16

2) x2 + 6x – 9

3) x2 + 5x + 25

4) x2 + 10x + 25

5) 4x2 – 20x + 25

6) x2 + 8x + 12

7) 49 – 14y + y2

8) 2x2 + 8x + 16

9) x2 – 2x – 3

10) x2 – 2x + 1

1) YES

2) NO -9

3) NO x•2•5 ≠ 5x

4) YES

5) YES

6) NO √12

7) YES

8) NO 2(x2 + 4x + 8)

9) NO √-3

10) YES

FACTOR practice time.

2 8 16r r 2( 4)r 249 28 4p p 2(7 2)p

2 24 12 9y yz z 2(2 3 )y z2 24 4x xy y 2(2 )x y281 180 100n n 2(9 10)n

Completing the Square

2 6 __x x

Take half of the middle term and square it to get the third term!

9 2 ___ 144c

2 12c 24c

24c

TOO:

2 2 ___a a 216 56 ___s s

2 2____ 49a b 29 ____ 25k

TOO FOR HOMEWORKfactor the perfect square trinomials

1) x2 – 18x + 81

2) 9x2 + 24xy + 16y2

3) 100 + 20x + x2

4) 4x2 + 4x + 1

5) x2 – 14x + 49

Homework

Perfect Square Trinomials Worksheet