\(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\\ =\left[\left(x^n\right)^2+x^ny^n+\left(y^n\right)^2\right]\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\\ =\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)=x^{6n}-y^{6n}\)

a: ta có: \(x\left(x-y\right)+y\left(x-y\right)\)

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

\(=x^2-y^2\)

b: Ta có: \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)

\(=x^n+x^{n-1}\cdot y-x^{n-1}\cdot y-y^n\)

\(=x^n-y^n\)

Ta có

D = x ( x 2 n - 1   +   y )   –   y ( x   +   y 2 n - 1 )   +   y 2 n   –   x 2 n   +   5

= x . x 2 n - 1   +   x . y   –   y . x   –   y . y 2 n - 1   +   y 2 n   –   x 2 n   +   5

= x 2 n   +   x y   –   x y   –   y 2 n   +   y 2 n   –   x 2 n   +   5

= ( x 2 n   –   x 2 n )   +   ( x y   –   x y )   +   ( y 2 n   –   y 2 n )   +   5

= 0 + 0 + 0 + 5 = 5

Đáp án cần chọn là: D

xn - 1(x + y) - y(xn - 1 + yn - 1)

= xn - x + y - yxn - y² n - 1

x(x – y) + y(x – y)

= x.x – x.y + y.x – y.y

= x2 – xy + xy – y2

= x2 – y2 + (xy – xy)

= x2 – y2

\(5\left(3x^{n+1}-y^{n-1}\right)-3\left(x^{n+1}+2y^{n-1}\right)+4\left(-x^{n+1}+2y^{n-1}\right)\)

\(=15x^{n+1}-5y^{n-1}-3x^{n+1}-6y^{n-1}-4x^{n+1}+8y^{n-1}\)

\(=8x^{n+1}-3y^{n-1}\)