Question

Phân tích đa thức thành nhân tử

2(x+y)(x-y)-(x-y)^2+(x+y)^2-4y^2

Answer 1

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

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

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

\(=\left(2y\right)^2-\left(2y\right)^2=0\)

Answer 2

Sửa:

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

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

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

\(=2x^2-6y^2+4xy\)

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

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

\(=2\left[x\left(x-y\right)+3y\left(x-y\right)\right]\)

\(=2\left(x-y\right)\left(3y+x\right)\)