1) \(5x^2y-30xy^2+45y^3=5y\left(x^2-6xy+9y^2\right)=5y\left(x+3y\right)^2\)
2) \(x^4-3x^3-24x+8=x^3\left(x-3\right)-8\left(x-3\right)=\left(x-3\right)\left(x^3-8\right)=\left(x-3\right)\left(x-2\right)\left(x^2+2x+4\right)\)
3) \(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)=x^2\left(y-z\right)+y^2\left(-y+z-x+y\right)+z^2\left(x-y\right)=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)=\left(y-z\right)\left(x^2-y^2\right)-\left(x-y\right)\left(y^2-z^2\right)=\left(y-z\right)\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(y-z\right)\left(y+z\right)=\left(x-y\right)\left(y-z\right)\left(x+y-y-z\right)=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
1: Ta có: \(5x^2y-30xy^2+45y^3\)
\(=5y\left(x^2-6xy+9y^2\right)\)
\(=5y\left(x-3y\right)^2\)
2: Ta có: \(x^4-3x^3-24x+8\)
\(=x^3\left(x-3\right)-8\left(x-3\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x^2+2x+4\right)\)
4: Ta có: \(6a^2-ab-2b^2+3a-2b\)
\(=6a^2-4ab+3ab-2b^2+3a-2b\)
\(=2a\left(3a-2b\right)+b\left(3a-2b\right)+\left(3a-2b\right)\)
\(=\left(3a-2b\right)\left(2a+b+1\right)\)
