1) Ta có: \(x^2-2x-9y^2+6y\)
\(=x^2-2x+1-9y^2+6y-1\)
\(=\left(x-1\right)^2-\left(3y-1\right)^2\)
\(=\left(x-1-3y+1\right)\left(x-1+3y-1\right)\)
\(=\left(x-3y\right)\left(x+3y-2\right)\)
3) Ta có: \(x^2-9-4xy+4y^2\)
\(=\left(x-2y\right)^2-3^2\)
\(=\left(x-2y-3\right)\left(x-2y+3\right)\)
4) Ta có: \(\left(a+b\right)^2-\left(a-b\right)^2\)
\(=\left(a+b-a+b\right)\left(a+b+a-b\right)\)
\(=2b\cdot2a=4ab\)
5) Ta có: \(\left(x+y\right)^3-3xy\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-3xy\right]\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-3xy\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\)
6) Ta có: \(\left(x-y\right)^3+3xy\left(x-y\right)\)
\(=\left(x-y\right)\left[\left(x-y\right)^2+3xy\right]\)
\(=\left(x-y\right)\left(x^2-2xy+y^2+3xy\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\)
7) Ta có: \(4x^2-12x-46\)
\(=\left(2x\right)^2-2\cdot2x\cdot3+9-55\)
\(=\left(2x-3\right)^2-55\)
\(=\left(2x-3-\sqrt{55}\right)\left(2x-3+\sqrt{55}\right)\)
