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: 4x2 - 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 |