Download IS IT A DIFFERENCE OF SQUARES?

Warmups – factor.
1) Write the prime factorization: 224
2) x2 +19x + 18
3) 49y2 + 56y + 16
4) 5xy + 15x + 4y + 12
10-4 Factoring
Difference of Squares
Objective: To identify and factor
binomials that are the difference
of two squares.
Standard 11.0
Remember…
a  2ab  b 
( a  b)
a  2ab  b 
( a  b)
2
2
2
2
2
2
Do you remember….
(a  b)(a  b) 
So….
a b
2
2
a  b  (a  b)(a  b)
2
2
Recognizing a
Difference of Squares
m  81
2
1st term is a perfect square
 2nd term is a perfect square
 Subtraction
 Answer… ( 1st  2nd )( 1st  2nd )
Example 1: Factor.

9 x  49
2
(3 x  7)(3 x  7)
LTT: IS IT A DIFFERENCE OF SQUARES?
If so… factor it.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
x2 – 4
9x2 – 1
2x2 – 4
2x2 – 8
x2 + y2
x3 – 25
9xy – y2
-16 + x2
-4 – 16x2
x4 – 81
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
YES --------------
YES --------------
NO
√2
YES 2(x2 – 4) -
NO
Adding
NO
x3
NO
x
YES x2 – 16 ---
NO
-(4 + 16x2)
YES √x4 = x2 ---
Example 2
20cd 2  125c5
1. Factor out the GCF:
5c
2. Rewrite the polynomial:
5c(4d  25c )
2
4
3. Factor the difference of squares inside of the
parenthesis:
2
2
5c(2d  5c )(2d  5c )
4. Don’t forget about the GCF on the outside 
TOO: Factor
1)
25x2 – 121
2)
16x4 – y2
3)
-98 + 2x2
4)
4x2 – 9y2
5)
3x3 – 12x
Factor & List which
process(es) you used.





GCF
Grouping
X-Box
Perfect Square Trinomial
Difference of Squares
y  6 y  16
2
24m  8
2
16 x  40 x  24
2
81x  16 y
4
4
n  2n  3mn  6m
2
Factor & List which
process(es) you used.





GCF
Grouping
X-Box
Perfect Square
Difference of Squares
15 x  45 y
2
2
1  8 p  16 p
2
t  t  t 1
3
2
4a  8a  4a
3
2
2 x  3x  5 x
3
2
Homework

Pg. 584 #22-39 all