Perfect Squares
Consider This
A perfect-square trinomial may be in the form a
​ ​ 2​1 2ab 1 b
​ ​ 2​
or ​a​ 2​2 2ab 1 b
​ ​ 2​. The first and last terms are perfect squares
and the middle term is twice the product of the square roots
of the first and last terms.
Factor the trinomial.
1 x​ ​ 2​1 8x 1 16
2 4​x​ 2​2 4x 1 1
3 9​x​ 2​2 36x 1 36
4 2​5x​ 2​1 100xy 1 10​0y​ 2​
5 1​6x​ 2​1 8x 1 16
6 x​ ​ 2​1 6x 1 9
7 36​x​ 2​2 84x 1 49
8 25​x​ 2 ​2 100xy 1 100​y​ 2​
9 64​x​  ​1 8x 1 __
​ 1 ​ 
10 36​x​  ​1 60x 1 25
​a​ 2​1 ​2ab​ ​1 ​b​ 2​
5 (a 1 b)​ ​ 2;​
11 x​ ​ 2​1 24x 1 144
12 x​ ​ 2​1 22x 1 121
​a​ 2​2 2ab 1 ​b​ 2​
5 (a 2 b)​ ​ 2​
2
4
2
Answer Box
A
B
not a perfect
square
G
s 
C
2
d
1 2
__
​​ 8x 1 ​ 2  ​  ​ ​ ​
2
(x 1 1​2)​  ​
H
2
(3x 2 6)​
​  ​
D
(x 1 ​3)​  ​
I
2
(x 1 11)​
​  ​
E
2
(2x 2 ​1)​  ​
F
2
(6x 1 ​5)​  ​
J
K
2
(5x 2 10y)​
​  ​
2
(5x 1 10y)​
​  ​
2
(6x 2 ​7)​  ​
L
2
(x 1 4)​
​  ​
Objective: Factor perfect-square trinomials.
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