Answer Key 7.6

  1. [latex](x^2-4y^2)(x^2+4y^2)[/latex]
    [latex](x-2y)(x+2y)(x^2+4y^2)[/latex]
  2. [latex](4x^2-9y^2)(4x^2+9y^2)[/latex]
    [latex](2x-3y)(2x+3y)(4x^2+9y^2)[/latex]
  3. [latex](x^2-16y^2)(x^2+16y^2)[/latex]
    [latex](x-4y)(x+4y)(x^2+16y^2)[/latex]
  4. [latex](25x^2-9y^2)(25x^2+9y^2)[/latex]
    [latex](5x-3y)(5x+3y)(25x^2+9y^2)[/latex]
  5. [latex](9x^2-4y^2)(9x^2+4y^2)[/latex]
    [latex](3x+2y)(3x-2y)(9x^2+4y^2)[/latex]
  6. [latex](x^2-9y^2)(x^2+9y^2)[/latex]
    [latex](x-3y)(x+3y)(x^2+9y^2)[/latex]
  7. [latex](25x^2-16y^2)(25x^2+16y^2)[/latex]
    [latex](5x-4y)(5x+4y)(25x^2+16y^2)[/latex]
  8. [latex](x^2-9y^2)(x^2+9y^2)[/latex]
    [latex](x-3y)(x+3y)(x^2+9y^2)[/latex]
  9. [latex](x^3-y^3)(x^3+y^3)[/latex]
    [latex](x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)[/latex]
  10. [latex](x^2)^3+(y^2)^3[/latex]
    [latex](x^2+y^2)(x^4-x^2y^2+y^4)[/latex]
  11. [latex](x^3-8y^3)(x^3+8y^3)[/latex]
    [latex](x-2y)(x^2+2xy+4y^2)(x+2y)(x^2-2xy+4y^2)[/latex]
  12. [latex](4x^2)^3+(y^2)^3[/latex]
    [latex](4x^2+y^2)(16x^4-4x^2y^2+y^4)[/latex]
  13. [latex](27x^3-y^3)(27x^3+y^3)[/latex]
    [latex](3x-y)(9x^2+3xy+y^2)(3x+y)(9x^2-3xy+y^2)[/latex]
  14. [latex](9x^2)^3+(y^2)^3[/latex]
    [latex](9x^2+y^2)(81x^4-9x^2y^2+y^4)[/latex]
  15. [latex](9x^2)^3+(4y^2)^3[/latex]
    [latex](9x^2+4y^2)(81x^4-36x^2y^2+16y^4)[/latex]
  16. [latex](8x^3-125y^3)(8x^3+125y^3)[/latex]
    [latex](2x-5y)(4x^2+10xy+25y^2)(2x+5y)(4x^2-10xy+25y^2)[/latex]
  17. [latex][(a+b)-(c-d)][(a+b)+(c-d)][/latex]
    [latex][a+b-c+d][a+b+c-d][/latex]
  18. [latex][(a+2b)-(3a-4b)][(a+2b)+(3a-4b)][/latex]
    [latex][a+2b-3a+4b][a+2b+3a-4b][/latex]
    [latex][-2a+6b][4a-2b][/latex]
    [latex]4[-a+3b][2a-b][/latex]
  19. [latex][(a+3b)-(2c-d)][(a+3b)+(2c-d)][/latex]
    [latex][a+3b-2c+d][a+3b+2c-d][/latex]
  20. [latex][(3a+b)-(a-b)][(3a+b)+(a-b)][/latex]
    [latex][2a+2b][4a][/latex]
    [latex]2[a+b][4a][/latex]
    [latex]8a(a+b)[/latex]
  21. [latex][(a+b)-(c-d)][(a+b)^2+(a+b)(c-d)+(c-d)^2][/latex]
    [latex][a+b-c+d][a^2+2ab+b^2+ac-ad+bc-bd+c^2-2cd+d^2][/latex]
  22. [latex][(a+3b)+(4a-b)][(a+3b)^2-(a+3b)(4a-b)+(4a-b)^2][/latex]
    [latex][5a+2b][a^2+6ab+9b^2-4a^2+ab-12ab+3b^2+16a^2-8ab+b^2][/latex]
    [latex][5a+2b][13a^2-13ab+13b^2][/latex]
    [latex]13[5a+2b][a^2-ab+b^2][/latex]

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