\(a.x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\) \(b.5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-y\right)\left(x-2\right)\) \(c.x^3-2x^2-4xy^2+x=x\left(x^2-2x+1-4y^2\right)=x\left[\left(x-1\right)^2-4y^2\right]=\left(x-1-2y\right)\left(x-1+2y\right)\) \(d.\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)
Đặt : \(x^2+7x+11=t\) , ta có :
\(\left(t+1\right)\left(t-1\right)-8=t^2-1-8=\left(t-3\right)\left(t+3\right)=\left(x^2+7x+8\right)\left(x^2+7x+14\right)\)
\(e.2x^2-5x-7=2x^2+2x-7x-7=2x\left(x+1\right)-7\left(x+1\right)=\left(x+1\right)\left(2x-7\right)\) \(f.x^2-12x+36=\left(x-6\right)^2=\left(x-6\right)\left(x-6\right)\)
\(g.x^4-5x^2+4=x^4-x^2-4x^2+4=x^2\left(x^2-1\right)-4\left(x^2-1\right)=\left(x^2-1\right)\left(x^2-4\right)=\left(x+1\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)\) \(g.a^3+b^3+c^3-3abc=\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)\)
