c: \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
d: \(81x^4+4y^2\)
\(=81x^4+4y^2+36x^2y-36x^2y\)
\(=\left(9x^2\right)^2+2\cdot9x^2\cdot2y+\left(2y\right)^2-36x^2y\)
\(=\left(9x^2+2y\right)^2-\left(6x\sqrt{y}\right)^2\)
\(=\left(9x^2-6x\sqrt{y}+2y\right)\left(9x^2+6x\sqrt{y}+2y\right)\)
e: \(x^2+3x-18\)
\(=x^2+6x-3x-18\)
\(=x\left(x+6\right)-3\left(x+6\right)\)
\(=\left(x+6\right)\left(x-3\right)\)
f: \(x^7+x^2+1\)
\(=x^7+x^6+x^5-x^6-x^5-x^4+x^4+x^3+x^2-x^3+1\)
\(=x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^2\left(x^2+x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)
a: \(x^2+2xy-8y^2+2xz+14yz-3z^2\)
\(=\left(x^2+y^2+z^2+2xy+2xz+2yz\right)-\left(9y^2-12yz+4z^2\right)\)
\(=\left(x+y+z\right)^2-\left(3y-2z\right)^2\)
\(=\left(x+y+z+3y-2z\right)\left(x+y+z-3y+2z\right)\)
\(=\left(x+4y-z\right)\left(x-2y+3z\right)\)
b: \(12x^2+5x-12y^2+12y-10xy-3\)
\(=12x^2+9x-18xy-4x-12y^2+8xy-3+6y-6y\)
\(=\left(12x^2-18xy+9x\right)-\left(4x-6y+3\right)+\left(8xy-12y^2+6y\right)\)
\(=3x\left(4x-6y+3\right)-\left(4x-6y+3\right)+2y\left(4x-6y+3\right)\)
\(=\left(4x-6y+3\right)\left(3x-1+2y\right)\)
