Answer Key 7.7

[latexpage]

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. \(-6\times -4=24\)
    \(-6+-4=-10\)
    \(2x^2-6x-4x+12\)
    \(2x(x-3)-4(x-3)\)
    \((x-3)(2x-4)\)