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1) \(x^6+1\)
\(=x^6+x^4-x^4+x^2-x^2+1\)
\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)
\(=x^2\left(x^4-x^2+1\right)+\left(x^4-x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
2) \(x^6-y^6\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(1,\)
\(x^2+x-12\)
\(=x^2-3x+4x-12\)
\(=x\left(x-3\right)+4\left(x-3\right)\)
\(=\left(x+4\right)\left(x-3\right)\)
\(2,\)
\(x^2-9x+20\)
\(=x^2-4x-5x+20\)
\(=x\left(x-4\right)-5\left(x-4\right)\)
\(=\left(x-5\right)\left(x-4\right)\)
\(3,\)
\(x^2+x-20\)
\(=x^2-4x+5x-20\)
\(=x\left(x-4\right)+5\left(x-4\right)\)
\(=\left(x+5\right)\left(x-4\right)\)
\(1)6x^2+7x-3\\=6x^2+9x-2x-3\\=3x(2x+3)-(2x+3)\\=(2x+3)(3x-1)\\2)5x^2+14x-3\\=5x^2+15x-x-3\\=5x(x+3)-(x+3)\\=(x+3)(5x-1)\)
1) \(6x^2+7x-3=6x^2+9x-2x-3=3x\left(x+3\right)-\left(2x+3\right)=\left(2x+3\right).\left(3x-1\right)\)
2) \(5x^2+14x-3=5x^2+15x-x-3=5x\left(x+3\right)-\left(x+3\right)=\left(x+3\right).\left(5x-1\right)\)
\(3x^2+10x+3=3x^2+9x+x+3=3x\left(x+3\right)+\left(x+3\right)\)
\(\Leftrightarrow\left(3x+1\right)\left(x+3\right)\)
a\(x^2-3xy-2y^2 =x^2-xy-2xy-2y^2 =x(x-y)-2y(x-y) =(x-2y)(x-y)\)