\(Bài10\)
\(a.x^2-y^2-2x+2y=\left(x+y\right)\left(x-y\right)+2\left(-x+y\right)\)
\(=\left(x+y\right)\left(x-y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right).\)
\(b.2x+2y-x^2-xy=\left(2x+2y\right)+\left(-x^2-xy\right)\)
\(=2\left(x-y\right)-x\left(x+y\right)=\left(x+y\right)\left(2-x\right).\)
\(c.3a^2-6ab+3b^2-12c^2=3\cdot a^2-3\cdot2ab+3\cdot b^2-3\cdot4c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right).\)
\(d.x^2-25+y^2+2xy=\left(x+y\right)^2-25=\left(x+y\right)^2-5^2\)
\(=\left(x+y+5\right)\left(x+y-5\right).\)
\(e.a^2+2ab+b^2-ac-bc=\left(a+b\right)\left(a+b-c\right).\)
\(f.x^2-2x-4y^2-4y=\left(x+2y\right)\left(x-2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right).\)
\(g.x^2y-x^3-9y+9x=\left(x^2y-x^3\right)+\left(9x-9y\right)=x^2\left(y-x\right)+9\left(x-y\right)\)
\(=x^2\left(y-x\right)-9\left(y-x\right)=\left(y-x\right)\left(x^2-9\right)=\left(y-x\right)\left(x+3\right)\left(x-3\right).\)
\(h.x^2\left(x-1\right)+16\left(1-x\right)=x^3-x^2+16-16x=\left(x^3-x^2\right)+\left(-16x+16\right)\)
\(=x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\left(x-1\right)\left(x+4\right)\left(x-4\right).\)