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Factor Special Products Worksheet

Factor Special Products Worksheet
  • Page 1
 1.  
Factor completely.
196tm2 - 448tm + 256t
a.
t(4m - 7)2
b.
4t(7m - 8)2
c.
4m(7m - 8)(7m + 8)
d.
4m(t - 7)2


Solution:

196tm2 - 448tm + 256t

= 4t(49m2 - 112m + 64)
[GCF is 4t.]

= 4t(7m - 8)2
[(a - b)2= a2 - 2ab + b2.]


Correct answer : (2)
 2.  
Express as a perfect square.
t2 + 14t + 49
a.
(t - 7)2
b.
(t + 9)2
c.
(t + 7)2
d.
t(t + 7)


Solution:

t2 + 14t + 49
[Given expression.]

= t2 + 2(t)(7) +72
[Write as (t2 + 2 t m +m2).]

= (t + 7)2
[Write as (t + m)2.]


Correct answer : (3)
 3.  
Express as a perfect square.
r2y2 + 6ry + 9
a.
(ry + 3.2)2
b.
(ry - 2.9)2
c.
(ry - 3)2
d.
(ry + 3)2


Solution:

r2y2 +6ry + 9
[Given expression.]

= (ry)2 + 2(ry)(3) +(3)2
[Write as (a2 + 2ab +b2).]

= (ry + 3)2
[Write as (a + b)2.]


Correct answer : (4)
 4.  
Express as a perfect square.
b2 - 10b + 25
a.
(b - 5)2
b.
(b + 6)2
c.
(b - 7)2
d.
(b + 5)2


Solution:

b2 - 10b + 25
[Given expression.]

= b2 - 2(b)(5) +52
[Write as (a2 - 2ab +b2).]

= (b - 5)2
[Write as (a - b)2.]


Correct answer : (1)
 5.  
Express as a perfect square.
z2 - 2.4z + 1.44
a.
(z + 1.2)2
b.
(z - 1.1)2
c.
(z + 1.4)2
d.
(z - 1.2)2


Solution:

z2 - 2.4z + 1.44
[Given expression.]

= z2-2(z)(1.2)+1.22
[Write as (a2-2ab+b2).]

= (z - 1.2)2
[Write as (a - b)2.]


Correct answer : (4)
 6.  
Express as a perfect square.
s2-14s6+4936
a.
(s -76)2
b.
(s -17)2
c.
(s +16)2
d.
(s +76)2


Solution:

s2-14s6+4936
[Given expression.]

= s2-2(s)(7)6+(76)2
[Write as (a2-2ab+b2).]

= (s -76)2
[Write as (a - b)2.]


Correct answer : (1)
 7.  
Express as a perfect square.
1r2+88r+1936
a.
(1r - 45)2
b.
(1r - 44)2
c.
(1r + 44)2
d.
(1r + 45)2


Solution:

1r2 +88r + 1936
[Original expression.]

Let 1r = h then 1r2 +88r + 1936 = h2 + 88h + 1936

= h2+2(h)(44)+442
[Write as (a2+2ab+b2).]

= (h + 44)2
[Write as (a + b)2.]

= (1r + 44)2
[Replace h with 1r.]


Correct answer : (3)
 8.  
Express as a perfect square.
p2 - 16p + 64
a.
(p + 9)2
b.
(p - 10)2
c.
(p - 8)2
d.
(p + 8)2


Solution:

p2 - 16p + 64
[Original expression.]

= p2-2(p)(8)+82
[Write as (a2-2ab+b2).]

= (p - 8)2
[Write as (a - b)2.]


Correct answer : (3)
 9.  
Express as a perfect square.
t2 - 16ta + 64a2
a.
(8t + a)2
b.
(t - 8a)2
c.
(8t - a)2
d.
(t + 8a)2


Solution:

t2 - 16ta + 64a2
[Original expression.]

= t2 - 2(t)(8a)+(8a)2
[Write as (a2 - 2ab +b2).]

= (t - 8a)2
[Write as (a - b)2.]


Correct answer : (2)
 10.  
Express as a perfect square: 0.25q2 - 5q + 25
a.
(0.5q - 0.6)2
b.
(0.5q - 5)2
c.
(0.5q + 5)2
d.
(5q - 5)2


Solution:

0.25q2 - 5q + 25
[Original expression.]

= (0.5q)2 - 2(0.5q)(5)+(5)2
[Write as (a2 - 2ab +b2).]

= (0.5q - 5)2
[Write as (a - b)2.]


Correct answer : (2)

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