a) Ta có: \(3x^2-7x^2-6x\)
\(=-4x^2-6x\)
\(=-2x\left(2x+3\right)\)
b) Ta có: \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)-8\)
\(=\left(x^2+3x\right)\cdot\left(x^2+3x+2\right)-8\)
Đặt \(t=x^2+3x\)
\(\Leftrightarrow\left(x^2+3x\right)\cdot\left(x^2+3x+2\right)-8=t\cdot\left(t+2\right)-8\)
\(=t^2+2t-8\)
\(=t^2+4t-2t-8\)
\(=t\left(t+4\right)-2\left(t+4\right)\)
\(=\left(t+4\right)\left(t-2\right)\)
\(=\left(x^2+3x+4\right)\left(x^2+3x-2\right)\)
c) Đặt \(a=x^2-5x\)
Ta có: \(\left(x^2-5x+1\right)^2-3\left(x^2-5x\right)-1\)
\(=\left(a+1\right)^2-3a-1\)
\(=a^2+2a+1-3a-1\)
\(=a^2-a\)
\(=a\left(a-1\right)\)
\(=\left(x^2-5x\right)\left(x^2-5x-1\right)\)
\(=x\left(x-5\right)\left(x^2-5x-1\right)\)
e) Ta có: \(x^2y-x^3-9y+9x\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(y-x\right)\left(x^2-9\right)\)
\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
