Question

[Vũ Ngọc Mẫn Nhi]

3x^n-2 ( x^n+2 - y^n+2) + y^n+2 ( 3x^n-2-y^n-2)

Answer 1

[Green sea lit named Wang Junkai]

$\text{Ta có :}$

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

$=3x^{n-2}\cdot x^{n+2}-3x^{n-2}\cdot y^{n+2}+y^{n+2}\cdot 3x^{n-2}-y^{n+2}\cdot y^{n-5}$

$=3x^{\left(n+2\right)+\left(n-2\right)}+\left(-3x^{n-2}\cdot y^{n+2}+y^{n+2}\cdot 3x^{n-2}\right)-y^{\left(n+2\right)+\left(n-5\right)}$

$=3x^{n+2+n-2}-y^{n+2+n-5}$

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

$=3x^{2n}-y^{2n-3}$