﻿ Factor Special Products Worksheet | Problems & Solutions
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Factor Special Products Worksheet
• Page 1
1.
Factor completely.
196$t$$m$2 - 448$t$$m$ + 256$t$ a. $t$(4$m$ - 7)2 b. 4$t$(7$m$ - 8)2 c. 4$m$(7$m$ - 8)(7$m$ + 8) d. 4$m$($t$ - 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.
$t$2 + 14$t$ + 49 a. b. c. 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.
$\frac{{r}^{2}}{{y}^{2}}$ + $\frac{6r}{y}$ + 9 a. b. c. d.

#### 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. a. b. c. d.

#### 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. a. b. c. d.

#### 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.
${s}^{2}-\frac{14s}{6}+\frac{49}{36}$ a. b. c. d.

#### 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.
$\frac{1}{{r}^{2}}+\frac{88}{r}+1936$ a. b. c. d.

#### 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. a. b. c. d.

#### 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.
${t}^{2}$ - 16ta + 64${a}^{2}$ a. b. c. d.

#### 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: ${0.25q}^{2}$ - 5q + 25 a. b. c. d.

#### 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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