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

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

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

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

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

\(=-x^2y^3\cdot2x^{n-2}y^n+x^2y^3\cdot3x^ny^{n-3}-x^2y^3\cdot x^{n-2}y^{n-3}\)

\(=-2x^ny^{n+3}+3x^{n+2}y^n-x^ny^n\)

=(a+b+c)(a2+b2+c2−ab−bc−ca)

=(a+b+c)(a2+2ab+b2−ab−ac+c2)−3ab(a+b+c)

=(a+b)3+c3−3ab(a+b+c)

=a3+3ab(a+b)+b3+c3−3abc−3ab(a+b

a3+b3+c3−3abc

A(x)=(1-x^n)(1+x^n)/(1-x)(1+x)

B(x)=1-x^n/1-x

A(x) chia hết cho B(x) khi 1-x^n chia hết cho 1+x

x^n+1/x+1=A(x)+(1+(-1)^n)/(x+1)

=>1-x^n chia hết cho 1+x khi và chỉ khi n=2k+1