Question

giúp mình chiều mai mình cần rồi cảm ơn rất nhiều

phân tích đa thức thành nhân tử:

1, x³-2x²+x

2, 2x²+4x+2-2y²

3, 2xy-x²-y²+16

4, x³+2x²y+xy²-9x

5, 2x-2y-x²+2xy-y²

Answer 1

\(1)x^3-2x^2+x\\ =x\left(x^2-2x+1\right)\\ =x\left(x-1\right)^2\\ 2)2x^2+4x+2-2y^2\\ =2\left(x^2+2x+1-y^2\right)\\ =2\left[\left(x+1\right)^2-y^2\right]\\ =2\left(x-y+1\right)\left(x+y+1\right)\\ 3)2xy-x^2-y^2+16\\ =16-\left(x^2-2xy+y^2\right)\\ =16-\left(x-y\right)^2=\left(x-y+4\right)\left(y-x+4\right)\\ 4)x^3+2x^2y+xy^2-9x\\ =x\left(x^2+2xy+y^2-9\right)\\ =x\left[\left(x+y\right)^2-9\right]\\ =x\left(x+y-3\right)\left(x+y+3\right)\\ 5)2x-2y-x^2+2xy-y^2\\ =\left(2x-2y\right)-\left(x^2-2xy+y^2\right)\\ =2\left(x-y\right)-\left(x-y\right)^2\\ =\left(x-y\right)\left(y-x+2\right)\)