Answer Key 7.3

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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. \(5\times 9=45\)
    \(5+9=14\)
    \(x^2+5xy+9xy+45y^2\)
    \(x(x+5y)+9y(x+5y)\)
    \((x+5y)(x+9y)\)