Answer Key 7.6

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