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Lời giải:
Ta có:
\(A=3x^{n-2}(x^{n+2}-y^{n+2})+y^{n+2}(3x^{n-2}-y^{n-2})\)
\(=3x^{n-2}.x^{n+2}-3x^{n-2}y^{n+2}+3y^{n+2}x^{n-2}-y^{n+2}.y^{n-2}\)
\(=3x^{n-2+n+2}-y^{n+2+n-2}=3x^{2n}-y^{2n}\)
\(3x^{n-2}\left(x^{n+2}-y^{n+2}\right)+y^{n+2}\left(3x^{n-2}-y^{2-2}\right)\)
\(=3x^{2n}-3x^{n-2}y^{n+2}+y^{n+2}\left(3x^{n-2}-y^{n-2}\right)\)
\(=3x^{2n}-3x^{n-2}y^{n+2}+3x^{n-2}y^{n+2}-y^{2n}\)
\(=3x^{2n}-y^{2n}\)
P/s: Mk ko rõ đề nên làm vậy nhé!
Đề bài chắc là đơn giản tỉ lệ thức(rút gọn) nên mình làm luôn nha:
\(3x^{n-2}\left(x^{n+2}-y^{n+2}\right)+y^{n+2}\left(3x^{n-2}-y^{n-2}\right)\)
\(=3x^{2n}-3xy^{2n}+3xy^2-y^{2n}\)
\(=3x^{2n}-y^{2n}\)
\(=3x^{n-2}.x^{n+2}-3x^{n-2}.y^{n+2}+y^{n+2}.3x^{n-2}-y^{n+2}.y^{n-2}\)
\(=3x^{2n}-y^{2n}\)
\(=3^{2n}-3x^{n-2}y^{n+2}+3x^{n-2}y^{n-2}-y^{2n}\)
\(=3x^{2n}-y^{2n}\)
1/
\(\dfrac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)
\(=\dfrac{x^3-3x^2y+3xy^2-y^3-3x^2y-3xy^2+y^3}{x-6y}\)
\(=\dfrac{x^3-6x^2y}{x-6y}\)
\(=\dfrac{x^2\left(x-6y\right)}{x-6y}\)
\(=x^2\)
\(2\)/
\(\dfrac{x^2+y^2+z^2-2xy+2xz-2yz}{x^2-2xy+y^2-z^2}\)
\(=\dfrac{\left(x-y+z^{ }\right)^2}{\left(x-y\right)^2-z^2}\)
\(=\dfrac{\left(x-y+z\right)^2}{\left(x-y-z\right)\left(x-y+z\right)}\)
\(=\dfrac{x-y+z}{x-y-z}\)
3/
\(\dfrac{\left(n+1\right)!}{n!\left(n+2\right)}\)
\(=\dfrac{n!\left(n+1\right)}{n!\left(n+2\right)}\)
\(=\dfrac{n+1}{n+2}\)
4/
\(\dfrac{n!}{\left(n+1\right)!-n!}\)
\(=\dfrac{n!}{n!\left(n+1\right)-n!}\)
\(=\dfrac{n!}{n!\left[\left(n+1\right)-1\right]}\)
\(=\dfrac{n!}{n!.n}\)
\(=\dfrac{1}{n}\)
5/
\(\dfrac{\left(n+1\right)!-\left(n+2\right)!}{\left(n+1\right)!+\left(n+2\right)!}\)
\(=\dfrac{\left(n+1\right)!-\left(n+1\right)!\left(n+2\right)}{\left(n+1\right)!+\left(n+1\right)!\left(n+2\right)}\)
\(=\dfrac{\left(n+1\right)!\left(-n-1\right)}{\left(n+1\right)!\left(n+3\right)}\)
\(=\dfrac{-n-1}{n+3}\)
