Factoring (Perfect Square Trinomials)
ChemistNATE
Factor each of the following perfect squares. If you can identify them as perfect squares, then you only
need ONE step to do each.
2
b)
x −18 x+81
2
d)
4 x +4 x+1
2
f)
p +8 pq+16 q
2
h)
k −20 k +100
2
j)
n +4 nj+4 j
2
l)
u −22 u+121
n)
r −2 r+1
p)
4 m +12 mw+9 w
a)
x +16 x+64
c)
m +2 m+1
e)
x −10 x+25
g)
w +20 q+100
i)
64 x +16 x+1
k)
25 f −40 f +16
m)
36 s −12 s+1
o)
100 x −42 x+121
2
2
2
2
2
2
2
2
2
2
2
2
2
Answers
Are the first and third terms perfect squares? If so, is the centre term exactly double the product
of the two? Then it's a perfect square. I've explained a few throughout.
a)
2
x +16 x+64
b)
First term: (x)2
Third term: (8)2
Second term: (8x) doubled.
2
x −18 x+81
(x-9)2
Therefore, it's a perfect square.
= (x+8)2
2
d)
4 x +4 x+1
=(2x+1)2
2
f)
p +8 pq+16 q
= (p+4q)2
2
h)
k −20 k +100
=(k-10)2
j)
n +4 nj+4 j
c)
m +2 m+1
=(m+1)2
e)
x −10 x+25
= (x-5)2
g)
w +20 q+100
= (w+10)2
i)
64 x +16 x+1
2
First term: (8x)2
Third term: (1)2
Second term: (8x) doubled.
Therefore it's a perfect square.
= (8x + 1)2
2
k)
25 f −40 f +16
= (5f – 4)2
m)
o)
100 x −42 x+121
= (10x – 11)2
2
2
2
2
2
2
First term: (n)2
Third term: (2j)2
Second term: (2nj) doubled
Therefore, it's a perfect square.
= (n+2j)2
2
l)
u −22 u+121
= (u-11)2
36 s −12 s+1
= (6s – 1)2
n)
r −2 r+1
(r - 1)2
2
p)
4 m +12 mw+9 w
= (2m + 3w)2
2
2
2
2