1)
\(x^3+2x^2+x\\ =x^3+x^2+x^2+x\\ =x^2\left(x+1\right)+x\left(x+1\right)\\ =\left(x+1\right)\left(x^2+x\right)\\ =x\left(x+1\right)\left(x+1\right)\)
2)
\(x^4-4x^3+4x^2\\ =x^2\left(x^2-4x+4\right)\\ =x^2\left(x-2\right)^2\\ =x.x\left(x-2\right)\left(x-2\right)\)
3)
\(5x^3-10x^2+5x\\ =5x^3-5x^2-5x^2+5x\\ =5x^2\left(x-1\right)-5x\left(x-1\right)\\ =\left(x-1\right)\left(5x^2-5x\right)\\ =5x\left(x-1\right)\left(x-1\right)\)
4)
\(2x^3-12x^2+18x\\ =2x\left(x^2-6x+9\right)\\ =2x\left(x-3\right)^2\\ =2x\left(x-3\right)\left(x-3\right)\)
5)
\(8x^2y-8xy+2x\\ =2x\left(4xy-4y+1\right)\)
6)
\(5x^2y-35xy+60y\\ =5y\left(xy-7x+12\right)\)
1: =x(x^2+2x+1)
=x(x+1)^2
2: =x^2(x^2-4x+4)
=x^2(x-2)^2
3: =5x(x^2-2x+1)
=5x(x-1)^2
4: =2x(x^2-6x+9)
=2x(x-3)^2
5: =2x(4xy-4y+1)
6: \(=5y\left(xy-7y+12\right)\)
