Question

phân tích đa thức thành nhân tử:

( x +y )³ - ( x - y )³

Answer 1

\(\left(x+y\right)^3-\left(x-y\right)^3\)

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

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

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

Answer 2

(x+y)³-(x-y)³

=(x+y-x+y)[(x+y)²+(x+y)(x-y)+(x-y)²]

=2y(x²+2xy+y²+x²-y²+x²-2xy-y²)

=2y(3x²-y²)