xin chào
\(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
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LT
19 tháng 4 2017
a) x (x - y) + y (x - y) = x2 – xy+ yx – y2
= x2 – xy+ xy – y2
= x2 – y2
b) xn – 1 (x + y) – y(xn – 1 + yn – 1) =xn+ xn – 1y – yxn – 1 - yn
= xn + xn – 1y - xn – 1y - yn
= xn – yn.
19 tháng 4 2017
Bài giải:
a) x (x - y) + y (x - y) = x2 – xy+ yx – y2
= x2 – xy+ xy – y2
= x2 – y2
b) xn – 1 (x + y) – y(xn – 1 + yn – 1) =xn+ xn – 1y – yxn – 1 - yn
= xn + xn – 1y - xn – 1y - yn
= xn – yn.
HV
20 tháng 11 2017
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/
\(\dfrac{\left(n+1\right)!-\left(n+2\right)!}{\left(n+1\right)!+\left(n+2\right)!}\)
\(=\dfrac{\left(n+1\right)!-\left(n+1\right)!\left(n+2\right)}{\left(n+1\right)!+\left(n+1\right)!\left(n+2\right)}\)
\(=\dfrac{\left(n+1\right)!\left(-n-1\right)}{\left(n+1\right)!\left(n+3\right)}\)
\(=\dfrac{-n-1}{n+3}\)
MT
19 tháng 8 2015
a) \(x\left(x-y\right)+y\left(x-y\right)\)
\(=x^2-xy+xy-y^2\)
\(=x^2-y^2\)
b) \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
\(=x^n+x^{n-1}y-x^{n-1}y-y^n\)
\(=x^n-y^n\)
Q
19 tháng 6 2017
a) \(\left(3x^{n+1}-y^{n-1}\right)-3\left(x^{n+1}+5y^{n-1}\right)-4\left(x^{n+1}+2y^{n-1}\right)\)
\(=3x^{n+1}-y^{n-1}-3x^{n+1}-15y^{n-1}+4x^{n+1}+8y^{n-1}\)
\(=-8y^{n-1}+4x^{n+1}\)
b) \(\left(\dfrac{3}{4}x^{n+1}-\dfrac{1}{2}y^n\right)\cdot2xy-\left(\dfrac{2}{3}x^{n+1}-\dfrac{5}{6}y^n\right)\cdot7xy\)
\(=\dfrac{3}{2}x^{n+2}y-xy^{n+1}+\left(-\dfrac{2}{3}x^{n+1}-\dfrac{5}{6}y^n\right)\cdot7xy\)
\(=\dfrac{3}{2}x^{n+2}y-xy^{n+1}-\dfrac{14}{3}x^{n+2}y+\dfrac{35}{6}xy^{n+1}\)
\(=-\dfrac{19}{6}x^{n+2}y+\dfrac{29}{6}xy^{n+1}\)
TD
19 tháng 6 2017
a)\(\left(3x^{n+1}-y^{n-1}\right)-3\left(x^{n+1}+5y^{n-1}\right)+4\left(x^{n+1}+2y^{n-1}\right)\)
\(=3x^{n+1}-y^{n-1}-3x^{n+1}-15y^{n-1}+4x^{n+1}+8y^{n-1}\)
\(=4x^{n+1}-8y^{n-1}\) \(\left(=4\left(x^{n+1}-2y^{n-1}\right)\right)\)
xn-1.x+xn-1.y-y.xn-1-y.yn-1
=xn-yn
\(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
= \(x^{n-2}+x^{n-1}y-x^{n-1}y+y^{n-2}\)
=\(x^{n-2}+y^{n-2}\)