\(x\left[\left(x+y\right)^2-\left(x-y\right)^2\right]\\ =x\left[\left(x+y-x+y\right)\left(x+y+x-y\right)\right]\\ =x.2y.2x\\ =4x^2y\)
\(x\left[\left(x+y\right)^2-\left(x-y\right)^2\right]\)
\(=x\left[x^2+2xy+y^2-\left(x^2-2xy+y^2\right)\right]\)
\(=x\left(x^2+2xy+y^2-x^2+2xy-y^2\right)\)
\(=x\cdot4xy\)
\(\)\(=4x^2y\)
\(x\left[\left(x+y\right)^2-\left(x-y\right)^2\right]\)
\(=x\left[x^2+2xy+y^2-x^2+2xy-y^2\right]\)
\(=x.4xy\)
\(=4x^2y\)