\(a,2x^2+4x+xy+2y\)
\(=\left(2x^2+xy\right)+\left(4x+2y\right)\)
\(=x\left(2x+y\right)+2\left(2x+y\right)\)
\(=\left(x+2\right)\left(2x+y\right)\)
\(b,x^2+xy-7x-7y\)
\(=\left(x^2+xy\right)+\left(-7x-7y\right)\)
\(=x\left(x+y\right)-7\left(x+y\right)\)
\(=\left(x-7\right)\left(x+y\right)\)
\(c,x^2+2xy+y^2-4\)
\(=\left(x+y\right)^2-2^2\)
\(=\left(x+y-2\right)\left(x+y+2\right)\)
\(d,1-y^3+6xy^2-12x^2y+8x^3\)
\(=1-\left(y^3-6xy^2+12x^2y-8x^3\right)\)
\(=1-\left(y-2x\right)^3\)
\(=1^3-\left(y-2x\right)^3\)
\(=\left(1-y+2x\right)\left(1+y-2x+y^2-4x^2\right)\)
\(e,b^2c+bc^2+ac^2-a^2c-ab\left(a+b\right)\)
\(=\left(b^2c+bc^2\right)+\left(ac^2-a^2c\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left(a-c\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)-ac\left(a+c\right)-ab\left(a+b\right)\)
\(=\left(bc-ac-ab\right)\left(b+c+a+c+a+b\right)\)
\(=\left(bc-ac-ab\right)\left(a+b+c\right)^2\)
\(f,x^3-x^2-5x+125\)
\(=\left(x^3+125\right)-x^2-5x\)
\(=x^3+15x^2+75x+125-x^2-5x\)
\(=x^3+14x^2+70x+125\)