1. Special Products Difference of Two Squares Perfect Square Trinomials

2. Bell Ringer:
Factor.
4x3 + 4x2 – 24x
4x (x2 + x – 6)
4x (x + 3)(x – 2)

3. LEQs:
How do you factor differences of squares? How do you factor perfect square trinomials?

4. Perfect Square Trinomials
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a  b)2
In order for a polynomial to be a perfect square
trinomial, two conditions must be satisfied:
1. The first and last terms must be perfect squares.
2. The “middle term” must equal 2 or – 2 times the product of the expressions being squared in the first and last term.

5. a = _____ , b = _____ , 2ab = _______
Perfect Square Trinomial Form: Example:
(Form 1)
a2 + 2ab + b2 = (a + b) x2 + 6x+ 9 = ____________ = (x + 3)2
a = _____ , b = _____ , 2ab = _______
(Form 2)
a2 – 2ab + b2 = (a  b)2 x2 – 10x + 25 = ____________ = (x 5)2
Condition 1:
First and last term are perfect squares.
Condition 1:
First and last term are perfect squares.

6. a = _____ , b = _____ , 2ab = _______
Perfect Square Trinomial Form: Example:
(Form 1)
a2 + 2ab + b2 = (a + b) x2 + 6x+ 9 = ____________ = (x + 3)2
a = _____ , b = _____ , 2ab = _______
(Form 2)
a2 – 2ab + b2 = (a  b)2 x2 – 10x + 25 = ____________ = (x 5)2
Condition 2:
The “middle term” must equal 2 or – 2 times the product of the expressions being squared in the first and last term.
Condition 2:
The “middle term” must equal 2 or – 2 times the product of the expressions being squared in the first and last term.

7. a = _____ , b = _____ , 2ab = _______
Perfect Square Trinomial Form: Example:
(Form 1)
a2 + 2ab + b2 = (a + b) x2 + 6x+ 9 = ____________ = (x + 3)2
a = _____ , b = _____ , 2ab = _______
(Form 2)
a2 – 2ab + b2 = (a  b)2 x2 – 10x + 25 = ____________ = (x 5)2

8. Perfect Square Trinomials
Examples: Factor.
The first term, x2, and third term, 16, are perfect squares.
1.) x2 + 8x + 16
The middle term, 8x, is 2 times the product of x and 4.
x2 + 8x + 16 = ____________ = (x + 4)2

9. Perfect Square Trinomials
2.) x2 – 14x + 49

10. Perfect Square Trinomials
3.) 9x4  30x2z + 25z2

11. Perfect Square Trinomials
4. 100a2 – 140ab + 49b2

12. Team Huddle Team Mastery

13. Difference of Two Squares
Difference of Squares Form: Example:
a2 – b2 = (a + b)(a  b) x2 – 64 = ( ____ ____ ) ( ____ ____ )
Check using FOIL:
Why do we call these DIFFERENCES What happens to the two middle of two squares? terms when we FOIL a
difference of two squares?

14. Difference of Two Squares
Example 1: Factor x2 – 4
Notice the terms are both perfect squares
and we have a difference
 difference of squares
x2 = (x)2
4 = (2)2
 x2 – 4 = (x)2 – (2)2
= (x – 2)(x + 2)
a2 – b2
= (a – b)(a + b)
factors as

15. Difference of Two Squares
Example 2: Factor 9p2 – 16
Notice the terms are both perfect squares
and we have a difference
 difference of squares
9p2 = (3p)2
16 = (4)2
 9a2 – 16 = (3p)2 – (4)2
= (3p – 4)(3p + 4)
a2 – b2
= (a – b)(a + b)
factors as

16. Difference of Two Squares
Example 3: Factor 2y6 – 50
Now it’s a difference of squares!
GCF First  2(y6 – 25)

17. Difference of Two Squares
Example 3: Factor 2y6 – 50
GCF First  2(y6 – 25)
Notice the terms are both perfect squares
and we have a difference
 difference of squares
y6 = (y3)2
25 = (5)2
 2(y6 – 25) = 2 ((y3)2 – (5)2)
= 2(y3 – 5)(y3 + 5)
2(a2 – b2)
= 2(a – b)(a + b)
factors as

18. Difference of Two Squares
Example 4: Factor 81 – x2y2
Notice the terms are both perfect squares
and we have a difference
 difference of squares
81 = (9)2
x2y2 = (xy)2
 81 – x2y2 = (9)2 – (xy)2
= (9 – xy)(9 + xy)
a2 – b2
= (a – b)(a + b)
factors as

19. Team Huddle Team Mastery

20. IXL Math Practice
Algebra 1 AA.5 Factor Quadratics: special cases

21. Quick Check:
Factor: 1. x x2 + 16x + 64

22. Groups:
Group 1 – Work on HW Individually Group 2 – Work on HW with me!