Answer Key 7.4

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1. \(-21\times 2=-42\)
   \(-21+2=-19\)
   \(7x^2-21x+2x-6\)
   \(7x(x-3)+2(x-3)\)
   \((x-3)(7x+2)\)
2. \(-6\times 4=-24\)
   \(-6+4=-2\)
   \(3n^2-6n+4n-8\)
   \(3n(n-2)+4(n-2)\)
   \((n-2)(3n+4)\)
3. \(14\times 1=14\)
   \(14+1=15\)
   \(7b^2+14b+b+2\)
   \(7b(b+2)+1(b+2)\)
   \((b+2)(7b+1)\)
4. \(-14\times 3=-42\)
   \(-14+3=-11\)
   \(21v^2-14v+3v-2\)
   \(7v(3v-2)+1(3v-2)\)
   \((3v-2)(7v+1)\)
5. \(15\times -2=-30\)
   \(15+-2=13\)
   \(5a^2+15a-2a-6\)
   \(5a(a+3)-2(a+3)\)
   \((a+3)(5a-2)\)
6. \(-20\times 2=-40\)
   \(-20+2=-18\)
   \(5n^2-20n+2n-8\)
   \(5n(n-4)+2(n-4)\)
   \((n-4)(5n+2)\)
7. \(-1\times -4=4\)
   \(-1+-4=-5\)
   \(2x^2-x-4x+2\)
   \(x(2x-1)-2(2x-1)\)
   \((2x-1)(x-2)\)
8. \(-6\times 2=-12\)
   \(-6+2=-4\)
   \(3r^2-6r+2r-4\)
   \(3r(r-2)+2(r-2)\)
   \((r-2)(3r+2)\)
9. \(14\times 5=70\)
   \(14+5=19\)
   \(2x^2+14x+5x+35\)
   \(2x(x+7)+5(x+7)\)
   \((x+7)(2x+5)\)
10. \(9\times -5=-45\)
    \(9+-5=4\)
    \(3x^2+9x-5x-15\)
    \(3x(x+3)-5(x+3)\)
    \((x+3)(3x-5)\)
11. \(-3\times 2=-6\)
    \(-3+2=-1\)
    \(2b^2-3b+2b-3\)
    \(b(2b-3)+1(2b-3)\)
    \((2b-3)(b+1)\)
12. \(8\times -3=-24\)
    \(8+-3=5\)
    \(2k^2+8k-3k-12\)
    \(2k(k+4)-3(k+4)\)
    \((k+4)(2k-3)\)
13. \(15\times 2=30\)
    \(15+2=17\)
    \(3x^2+15xy+2xy+10y^2\)
    \(3x(x+5y)+2y(x+5y)\)
    \((x+5y)(3x+2y)\)
14. \(-7\times 5=-35\)
    \(-7+5=-2\)
    \(7x^2-7xy+5xy-5y^2\)
    \(7x(x-y)+5y(x-y)\)
    \((x-y)(7x+5y)\)
15. \(15\times -4=-60\)
    \(15+-4=11\)
    \(3x^2+15xy-4xy-20y^2\)
    \(3x(x+5y)-4y(x+5y)\)
    \((x+5y)(3x-4y)\)
16. \(18\times -2=-36\)
    \(18+-2=16\)
    \(12u^2+18uv-2uv-3v^2\)
    \(6u(2u+3v)-v(2u+3v)\)
    \((2u+3v)(6u-v)\)
17. \(-16\times -1=16\)
    \(-16+-1=-17\)
    \(4k^2-16k-k+4\)
    \(4k(k-4)-1(k-4)\)
    \((k-4)(4k-1)\)
18. \(7\times -4=-28\)
    \(7+-4=3\)
    \(4r^2+7r-4r-7\)
    \(r(4r+7)-1(4r+7)\)
    \((4r+7)(r-1)\)
19. \(-12\times 3=-36\)
    \(-12+3=-9\)
    \(4m^2-12mn+3mn-9n^2\)
    \(4m(m-3n)+3n(m-3n)\)
    \((m-3n)(4m+3n)\)
20. \(\text{Cannot be factored.}\)
21. \(12\times 1=12\)
    \(12+1=13\)
    \(4x^2+12xy+xy+3y^2\)
    \(4x(x+3y)+y(x+3y)\)
    \((x+3y)(4x+y)\)
22. \(8\times -3=-24\)
    \(8+-3=5\)
    \(6u^2+8uv-3uv-4v^2\)
    \(2u(3u+4v)-v(3u+4v)\)
    \((3u+4v)(2u-v)\)
23. \(20\times -1=-20\)
    \(20+-1=19\)
    \(10x^2+20xy-xy-2y^2\)
    \(10x(x+2y)-1(x+2y)\)
    \((x-2y)(10x-y)\)
24. \(-15\times 2=-30\)
    \(-15+2=-13\)
    \(6x^2-15xy+2xy-5y^2\)
    \(3x(2x-5y)+y(2x-5y)\)
    \((2x-5y)(3x+y)\)