Easy Algebra Step-by-Step

224 Answer Key

1. False


2. False


3. False


4. False


5. False


6. − a − b
   = −1a − 1b
   = −1(a + b)
   = −(a + b)


7. −3x^2 + 6 x − 9
   = −3 ⋅ x^2 − 3 ⋅ −2x − 3 ⋅ 3
   = −3(x^2 − 2x + 3)


8. 3 − x
   = −1x + 3
   = −1 ⋅ x −1 ⋅ −3
   = −1(x − 3)
   = −(x − 3)


9. 24x^9 y^2 − 6x^6 y^7 z^4
   = 6 x^6 y^2 ⋅ 4 x^3 − 6x^6 y^2 ⋅ y^5 z^4
   = 6 x^6 y^2 (4x^3 − y^5 z^4 )


10. −45x^2 + 5
    = −5 ⋅ 9 x^2 − 5 ⋅ −1
    = −5(9x^2 − 1)
    = −5(3x + 1)(3x − 1)


11. a^3 b − ab + b
    = b(a^3 − a + 1)


12. 14x + 7 y
    = 7 ⋅ 2 x + 7 ⋅ y
    = 7(2x + y)
    13. x(2x − 1) + 3(2x − 1)
    = (2x − 1)(x + 3)
    14. y(a + b) + (a + b)
    = (a + b)(y + 1)
    15. x(x − 3) + 2(3 − x)
    = x(x − 3) − 2(x − 3)
    = (x − 3)(x − 2)
    16. cx + cy + ax + ay
    = c(x + y)+ a(x + y)
    = (x + y)(c + a)
    17. x^2 − 3x − 4 = (x − 4)(x + 1)
    18. x^2 − 49 = (x + 7)(x − 7)
    19. 6x^2 + x − 15 = (3x + 5)(2x − 3)
    20. 16x^2 − 25y^2 = (4x + 5 y)(4x − 5y)
    21. 27x^3 − 64 = (3x − 4)(9x^2 + 12 x + 16)
    22. 8a^3 + 125 b^3 = (2a + 5 b)(4a^2 − 10ab +
    25 b^2 )
    23. 2x^4 y^2 z^3 − 32x^2 y^2 z^3
    = 2 x^2 y^2 z^3 ⋅ x^2 − 2x^2 y^2 z^3 ⋅ 16
    = 2 x^2 y^2 z^3 (x^2 − 16)
    = 2 x^2 y^2 z^3 (x + 4)(x − 4)
    24. a^2 (a + b) − 2ab(a + b) + b^2 (a + b)
    = (a + b)(a^2 − 2ab + b^2 )
    = (a + b)(a − b)^2

Chapter 12 Factoring Polynomials

Exercise 12