Question

1, phân tích đa thức thành nhân tử

a, x^2-2xy+y^2-81          b , 2x^3y-2xy^3-4xy^2-2xy

c , x^3-2x^2+x                 d, 2x^2+4x+2-2y^2

e,2xy-x^2-y^2+16

Answer 1

\(x^2-2xy+y^2-81=\left(x-y\right)^2-81=\left(x-y-9\right)\left(x-y+9\right)\)

\(2x^3y-2xy^3-4xy^2-2xy=2xy\left(x^2-y^2-2y-1\right)=2xy\left(x^2-\left(y+1\right)^2\right)\)

\(=2xy\left(x+y+1\right)\left(x-y-1\right)\)

\(x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\)

\(2x^2+4x+2-2y^2=2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]=2\left(x-y+1\right)\left(x+y+1\right)\)

\(2xy-x^2-y^2+16=16-\left(x-y\right)^2=\left(4-x+y\right)\left(4+x-y\right)\)