Question

cmr a²ⁿ⁺¹+b²ⁿ⁺¹ bằng (a+b)(a²ⁿ-a^2n-1.b+a^2n-2.b²+...+a²ⁿ.b^2n-2-a.b²ⁿ

Answer 1

Ta có:

\(VP=\left(a+b\right)\left(a^{2n}-a^{2n-1}.b+a^{2n-2}.b^2+...+a^{2n}.b^{2n-2}-a.b^{2n-1}+b^{2n}\right)\)

\(=a^{2n+1}-a^{2n}.b+a^{2n-1}b^2+...+a^2.b^{2n-1}+a.b^{2n}+a^{2n}.b-a^{2n-1}.b^2+....-a.b^{2n}+b^{2n+1}\)

\(=a^{2n+1}+b^{2n+1}=VT\)

Vậy.....................(đpcm)

Chúc bạn học tốt!!!

Answer 2

Ta có:VT=\(\left(a+b\right)\left(a^{2n}-a^{2n-1}b+...-b^{2n}\right)\)

=\(a^{2n+1}-a^{2n}b+...+a^{2n}b+b^{2n}\)(Triệt tiêu hết )

=\(a^{2n+1}+b^{2n+1}\)(đpcm)