MTH 030 -- Elementary Algebra -- Exercise Solutions
Section:
5.4

26)  Factor x2 + 10x + 25
       Solution:  
x2 + 10 x + 25 = (x + 5)2
Square of a Sum
28)  Factor z 2- 2z + 1
       Solution:  
z2 - 2z + 1 = (x - 1)2
Square of a Difference
30)  Factor r2 + 24x + 144
       Solution:  
r2 + 24 x + 144 = (r + 12)2
Square of a Sum
32)  Factor v2 - 14v + 49
       Solution:  
v2 - 14v + 49 = (v - 7)2
Square of a Difference
34)  Factor 4x2 - 4x + 1
       Solution:  4
x2 - 4x + 25 = (2x - 1)2
Square of a Difference
36)  Factor 4x2 + 10x + 25
       Solution:  
x2 - 20 x + 25 = (2x - 5)2
Square of a Difference
38)  Factor a2 - 2ab + b2
       Solution:  
a2 - 2ab + b2 = (a - b)2
Square of a Difference
40)  Factor 25x2 + 20xy + 4y2
       Solution: 
25x2 + 20xy + 4y2 = (5x + 2y)2
Square of a Sum
46)  Factor x2 - 25
       Solution: 
x2 - 25 = (x + 5)(x - 5)
Difference of Squares
48)  Factor 9z2 - 1
       Solution: 
x2 - 25 = (3z + 1)(3z - 1)

Difference of Squares
50)  Factor 4x2 - z2
       Solution: 
4x2 - z2 = (2x + z)(2x - z)

Difference of Squares
52)  Factor 36a2 - 121b2
       Solution: 
36a2 - 121b2 = (6a + 11b)(6a - 11b)
Difference of Squares
54)  Factor 121a2 + 144b2
       Solution: 
121a2 + 144b2 is prime
Sum of Two Squares is Prime
56)  Factor 81y2 - 100z2
       Solution: 
81y2 - 100z2 = (9y - 10z)(9y + 10z)
Difference of Squares
58)  Factor 900 - B2C2
       Solution: 
900 - B2C2 = 302 - (BC)2 = (30 + BC)(30 - BC)
Difference of Squares
60)  Factor 2a2 - 200b2
       Solution: 
2a2 - 200b2 = 2(a2 - 100b2)
                          = 2(a - 10b)(a + 10 b)
Factor out the common factor then
Factor the Difference of Squares
62)  Factor 20x2 - 5
       Solution: 
20x2 - 5 = 5(4x2 - 1) = 5(2x + 1)(2x - 1)
Factor out the common factor then
Factor the Difference of Squares
64)  Factor 4b2y - 16c2y
       Solution: 
4b2y - 16c2y = 4y(b2 -4c2)
                         = 4y(b - 2c)(b + 2c)
Factor out the common factor then
Factor the Difference of Squares
66)  Factor y4 - 625
       Solution: 
y4 - 625 = (y2) - 252 = (y2 + 25)(y2 - 25)
                          (y2 + 25)(y - 5)(y + 5)
Difference of Squares -- Used twice
68)  Factor b4 - 256
       Solution: 
b4 - 256 = (b2 + 16)(b2 - 16)
                           =(b2 + 16)(b - 4)(b + 4)
Difference of Squares -- Used twice
70)  Factor 16y8 - 81z4
       Solution: 
16y8 - 81z4 = (4y4)2 - (9z2)2
= (4y4 + 9z2)(4y4- 9z2) = (4y4 + 9z2)(2y2+ 3z)(2y2- 3z)
Difference of Squares -- Used twice