\(\left(\left(x+y\right)^2\right)^3+\left(\left(x-y\right)^2\right)^3\)
\(=\left(\left(x+y\right)^2+\left(x-y\right)^2\right)\left(\left(x+y\right)^4-\left(x^2-y^2\right)^2+\left(x-y\right)^4\right)\)
\(=\left(2x^2+2y^2\right)\left(\left(x+y\right)^4-\left(x^2-y^2\right)^2+\left(x-y\right)^4\right)\)
\(=2\left(x^2+y^2\right)\left(\left(x+y\right)^4-\left(x^2-y^2\right)^2+\left(x-y\right)^4\right)⋮\left(x^2+y^2\right)\)
\(\left(x+y\right)^6+\left(x-y\right)^6\)
\(=\left[\left(x+y\right)^2\right]^3+\left[\left(x-y\right)^2\right]^3\)
\(=\left[\left(x+y\right)^2+\left(x-y\right)^2\right]\left(...\right)\)
\(=\left(x^2+2xy+y^2+x^2-2xy+y^2\right)\left(...\right)\)
\(=\left(2x^2+2y^2\right)\left(...\right)\)
\(=2\left(x^2+y^2\right)\left(...\right)⋮x^2+y^2\left(đpcm\right)\)
