4 D2PS.notebook
January 05, 2016
Do Now:
Find the product:
1) (x + 8)(x - 8)
2) (10 + x)(10 - x)
Homework Answers
1) 2x(x ­ 5) 6) 3a2(1 + 4a2)
11) x2y2(x + y)
2) 4c(c + 3)
7) 7u2(2 + 5u2)
12) 3x(x2 + x + 2)
3) 2m(4m2 ­ 1)
8) 15x2(x3 ­ 2)
13) 5a(a3 ­ a + 5)
4) 5m2(2m3 + 5)
9) 4a2(4a ­ 3)
14) 3x(2x2 + xy + y)
5) 6d(d ­ 4)
10) a2b(a2b ­ 1)
15) 5x(x2 + x ­ 2)
4 D2PS.notebook
January 05, 2016
date:
Factoring:
Difference of
Two Perfect
Squares
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.
4 D2PS.notebook
January 05, 2016
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
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
4 D2PS.notebook
January 05, 2016
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
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.
4 D2PS.notebook
January 05, 2016
Write the expression in factored form.
1) x2 - 81
2) x2 - 64
3) x2 - 1
4) x2 - 4
5) x2 - 16
6) x2 - 49
7) x2 - 36
8) x2 - 25
4 D2PS.notebook
January 05, 2016
9) x2 - 9
10) 4x2 - 25
11) x2 - 81y2
12) 9x2 - 4
13) x2 - 64y2
14) 36x2 - 49y2
15) 100x2 - 1
16) 9x2 - 25y2
4 D2PS.notebook
17) 4x2 - 81
19) 36 - y2
21) 196y2 - 25
January 05, 2016
18) 49 - x2
20) x2 - y2
4 D2PS.notebook
January 05, 2016
Practice:
1) x2 - 64
3) y2 - 25
2) c2 - 81
4) m2 - 169
5) b2 - 1
6) 100 - r2
7) a2 - b2
8) x2 - y2
4 D2PS.notebook
January 05, 2016
9) 16p2 - 9
10) 144h2 - 121
11) 81k2 - 400m2
12) 4x2 - 25y2
13) 49x6 - y2
15) a2 b2 - 225
14) x2 y2 - 1
16) c2 d2 - m2 n2
4 D2PS.notebook
17) r10 - s6
19) 16x4 y2 - 9b2
January 05, 2016
18) 64 - d2
20) 25x2 - 81y4