Answer Key 7.7

  1. 6a(4c-3b)+15d(4c-3b)
    (4c-3b)(6a+15d)
    3(4c-3b)(2a+5d)
  2. -6\times -5=30
    -6+-5=-11
    2x^2-6x-5x+15
    2x(x-3)-5(x-3)
    (x-3)(2x-5)
  3. -5\times -4=20
    -5+-4=-9
    5u^2-5uv-4uv+4v^2
    5u(u-v)-4v(u-v)
    (u-v)(5u-4v)
  4. (4x+6y)^2
  5. -2(x^3-64y^3)
    -2(x-4y)(x^2+4xy+16y^2)
  6. 20u(v-3u^2)-5x(v-3u^2)
    (v-3u^2)(20u-5x)
  7. 2(27u^3-8)
    2(3u-2)(9u^2+6u+4)
  8. 2(27-64x^3)
    2(3-4x)(9+12x+16x^2)
  9. n(n-1)
  10. -25\times 3=-75
    -25+3=-22
    5x^2-25x+3x-15
    5x(x-5)+3(x-5)
    (x-5)(5x+3)
  11. x^2-3xy-xy+3y^2
    x(x-3y)-y(x-3y)
    (x-3y)(x-y)
  12. -15\times -15=225
    -15+-15=-30
    5(9u^2-30uv+25v^2)
    5(9u^2-15uv-15uv+25v^2)
    5(3u(3u-5v)-5v(3u-5v))
    5(3u-5v)(3u-5v)
  13. (m-2n)(m+2n)
  14. 3(4ab-6a+2nb-3n)
    3(2a(2b-3)+n(2b-3))
    3(2b-3)(2a+n)
  15. 36b^2c-24b^2d+24ac-16ad
    12b^2(3c-2d)+8a(3c-2d)
    (3c-2d)(12b^2+8a)
    4(3c-2d)(3b^2+2a)
  16. -4\times 2=-8
    -4+2=-2
    3m(m^2-2mn-8n^2)
    3m(m^2-4mn+2mn-8n^2)
    3m(m(m-4n)+2n(m-4n))
    3m(m-4n)(m+2n)
  17. 2(64+27x^3)
    2(4+3x)(16-12x+9x^2)
  18. (4m+3n)(16m^2-12mn+9n^2)
  19. 5\times 2=10
    5+2=7
    n(n^2+7n+10)
    n(n^2+5n+2n+10)
    n(n(n+5)+2(n+5))
    n(n+5)(n+2)
  20. (4m-n)(16m^2+4mn+n^2)
  21. (3x-4)(9x^2+12x+16)
  22. (4a-3b)(4a+3b)
  23. x(5x+2)
  24. -6\times -4=24
    -6+-4=-10
    2x^2-6x-4x+12
    2x(x-3)-4(x-3)
    (x-3)(2x-4)

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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