Answer Key 7.3

  1. 9\times 8 = 72
    9+8=17
    p^2+9p+8p+72
    p(p+9)+8(p+9)
    (p+9)(p+8)
  2. 9\times -8=-72
    9+-8=1
    x^2+9x-8x-72
    x(x+9)-8(x+9)
    (x+9)(x-8)
  3. -8\times -1 = 8
    -8+-1=-9
    n^2-n-8n+8
    n(n-1)-8(n-1)
    (n-1)(n-8)
  4. 6\times -5 = -30
    6+-5=1
    x^2+6x-5x-30
    x(x+6)-5(x+6)
    (x+6)(x-5)
  5. -10\times 1 = -10
    -10+1=-9
    x^2-10x+x-10
    x(x-10)+1(x-10)
    (x-10)(x+1)
  6. 8\times 5 = 40
    8+5=13
    x^2+8x+5x+40
    x(x+8)+5(x+8)
    (x+8)(x+5)
  7. 4\times 8 =32
    4+8=12
    b^2+4b+8b+32
    b(b+4)+8(b+4)
    (b+4)(b+8)
  8. -7\times -10=70
    -7+-10=-17
    b^2-7b-10b+70
    b(b-7)-10(b-7)
    (b-7)(b-10)
  9. -3\times -5=15
    -3+-5=-8
    u^2-3uv-5uv+15v^2
    u(u-3v)-5v(u-3v)
    (u-3v)(u-5v)
  10. -8\times 5 =-40
    -8+5=-3
    m^2-8mn+5mn-40n^2
    m(m-8n)+5n(m-8n)
    (m-8n)(m+5n)
  11. 4\times -2=-8
    4+-2=2
    m^2+4mn-2mn-8n^2
    m(m+4n)-2n(m+4n)
    (m+4n)(m-2n)
  12. 8\times 2=16
    8+2=10
    x^2+8xy+2xy+16y^2
    x(x+8y)+2y(x+8y)
    (x+8y)(x+2y)
  13. -9\times -2=18
    -9+-2=-11
    x^2-9xy-2xy+18y^2
    x(x-9y)-2y(x-9y)
    (x-9y)(x-2y)
  14. -2\times -7=14
    -2+-7=-9
    u^2-2uv-7uv+14v^2
    u(u-2v)-7v(u-2v)
    (u-2v)(u-7v)
  15. 4\times -3=-12
    4+-3=1
    x^2+4xy-3xy-12y^2
    x(x+4y)-3y(x+4y)
    (x+4y)(x-3y)
  16. 5\times 9=45
    5+9=14
    x^2+5xy+9xy+45y^2
    x(x+5y)+9y(x+5y)
    (x+5y)(x+9y)

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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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