Question

[Phạm Ánh Tuyết]

Rút gọn:

3x^n-2.(xⁿ⁺²-yⁿ⁺²)+yⁿ⁺².(3x^n-2-y^n-5) (n\(\varepsilon N;n\ge2\))

Answer 1

[Đức Hiếu]

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

\(=3x^{n-2}.x^{n+2}-3x^{n-2}.y^{n+2}+y^{n+2}.3x^{n-2}-y^{n+2}.y^{n-5}\)

\(=3x^{2n}-\left(3xy\right)^{n-2}.y^4+\left(3xy\right)^{n-2}.y^4-y^{2n-3}\)

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

Chúc bạn học tốt!!!

Answer 2

[Trần Quốc Lộc]

\(\text{Ta có : }\)

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

\(\\ =3x^{n-2}\cdot x^{n+2}-3x^{n-2}\cdot y^{n+2}+y^{n+2}\cdot3x^{n-2}-y^{n+2}\cdot y^{n-5}\)

\(\\ =3x^{\left(n+2\right)+\left(n-2\right)}+\left(-3x^{n-2}\cdot y^{n+2}+y^{n+2}\cdot3x^{n-2}\right)-y^{\left(n+2\right)+\left(n-5\right)}\)

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

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

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