3 D2PS.notebook
January 07, 2015
Do Now:
Find the product:
1) (x + 8)(x - 8)
2) (10 + x)(10 - x)
date:
Factoring:
Difference of
Two Perfect
Squares
3 D2PS.notebook
January 07, 2015
Our goal is to figure out what two
factors multiply to give you the product.
(x + 8)(x - 8) = x 2 - 64
factors
product
(10 + x)(10 - x) = 100 - x 2
factors
product
This type of factoring is called the
Difference of Two Perfect Squares.
How do you know if it is Difference of Two
Perfect Squares?
Both (two) terms must be perfect squares and
there must be a minus sign between them.
minus
x2 - 64
perfect square
perfect square
minus
100 - x2
perfect square
perfect square
3 D2PS.notebook
January 07, 2015
Don't forget the perfect squares:
1x1 = 1
√1 = 1
2x2 = 4
√4 = 2
3x3 = 9
√9 = 3
4x4 = 16
√16 = 4
5x5 = 25
√25 = 5
6x6 = 36
√36 = 6
7x7 = 49
√49 = 7
8x8 = 64
√64 = 8
9x9 = 81
√81 = 9
10x10 = 100
√100= 10
therefore
Any variable with an even exponent
is a perfect square.
•
•
•
•
x2 = x1 ∙ x1 = (x)²
a4 = a² ∙ a²= (a²)²
z6 = z³∙ z³= (z³)²
g34 = g17 ∙ g17 = (g17 )²
so √x2 =
so √a4 =
so √z6 =
so √g34 =
• Note: divide the even exponent by 2
3 D2PS.notebook
January 07, 2015
When factoring a polynomial first look for aGCF then
look for the Difference of Two Perfect Squares
(D2PS).
To Factor using D2PS
1) Draw 2 sets ( )‛s
one + one ( + )( - )
2) Take the square root of each term.
3) Place each root into both sets of
parentheses.
4) Check by (Double) distributing.
Write the expression in factored form.
1) x2 - 81
3) x2 - 1
2) x2 - 64
4) x2 - 4
3 D2PS.notebook
January 07, 2015
5) x2 - 16
6) x2 - 49
7) x2 - 36
8) x2 - 25
9) x2 - 9
10) 4x2 - 25
11) x2 - 81y2
12) 9x2 - 4
3 D2PS.notebook
January 07, 2015
13) x2 - 64y2
14) 36x2 - 49y2
15) 100x2 - 1
16) 9x2 - 25y2
17) 4x2 - 81
19) 36 - y2
18) 49 - x2
20) x2 - y2
3 D2PS.notebook
January 07, 2015
21) 196y2 - 25
Practice:
1) x2 - 64
3) y2 - 25
2) c2 - 81
4) m2 - 169
3 D2PS.notebook
January 07, 2015
5) b2 - 1
6) 100 - r2
7) a2 - b2
8) x2 - y2
9) 16p2 - 9
10) 144h2 - 121
11) 81k2 - 400m2
12) 4x2 - 25y2
3 D2PS.notebook
13) 49x6 - y2
15) a2 b2 - 225
17) r10 - s6
19) 16x4 y2 - 9b2
January 07, 2015
14) x2 y2 - 1
16) c2 d2 - m2 n2
18) 64 - d2
20) 25x2 - 81y4