bài `5` : rút gọn bth
`a)x(x-y)+y(x-y)`
`b) x^(n-1) (x+y)-y(x^(n-1) +y^(n-1))`
Rút gọn biểu thức
a) x ( x - y ) + y ( x - y )
b) x^n-1 ( x + y ) - y ( x^n-1 + y^n-1 )
a, x(x-y)+y(x-y)
=x2-xy+xy-y2
=x2-y2
b, xn-1(x+y)-y(xn-1+yn-1)
=xn+xn-1y-xn-1y-yn
=xn-yn
Chúc bn học giỏi nhoa!!!
Rút gọn biểu thức:
a) x ( x – y ) + y ( x – y )
b) xn – 1 ( x + y ) – y( xn – 1 + yn – 1 ).
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.
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.
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.
Cho biểu thức N = \(\left(\dfrac{x^2}{x^2-y^2}+\dfrac{y}{x-y}\right):\dfrac{x^3-y^3}{x^5-x^4y-xy^4+y^5}\)
a. Rút gọn N
b. TÍnh giá trị của N biết xy = 1; x + y = 0
\(a,N=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{\left(x-y\right)\left(x^4-y^4\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\\ N=\dfrac{\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)}{\left(x-y\right)\left(x+y\right)}=x^2+y^2\\ b,N=\left(x+y\right)^2-2xy=0-2\cdot1=-2\)
Cho biểu thức N = \(\left(\dfrac{x^2}{x^2-y^2}+\dfrac{y}{x-y}\right):\dfrac{x^3-y^3}{x^5-x^4y-xy^4+y^5}\)
a. Rút gọn N
b. TÍnh giá trị của N biết xy = 1; x + y = 0
ĐKXĐ: \(x\ne y\)
a) \(N=\dfrac{x^2+y\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}:\dfrac{\left(x-y\right)\left(x^2+xy+y^2\right)}{x^4\left(x-y\right)-y^4\left(x-y\right)}=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x+y\right)}.\dfrac{\left(x-y\right)^2\left(x+y\right)\left(x^2+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}=x^2+y^2\)
b) \(x+y=0\Leftrightarrow\left(x+y\right)^2=0\Leftrightarrow x^2+y^2-2xy=0\)
\(\Leftrightarrow N=x^2+y^2=0+2xy=2.1=2\)
9 Rút gọn biểu thức: a) 2x(2x-y)+2y(x-2y); b) x(x^n-1+y^n-1)-y^n-1(x-y)
a)2x(2x-y)+2y(x-2y)=\(4x^2-2xy+2xy-4y^2=4x^2-4y^2.\)
b)\(x\left(x^{n-1}+y^{n-1}\right)-y^{n-1}\left(x-y\right)\)=\(x^n+y^n-y^n+y^n=x^n+y^n\)
Rút gọn biểu thức: x^n-1 (x + y) - y (x^n-1 + y^n-1
Mik viết lại hộ cho :
\(x^{n-1}\).\(\left(x+y\right)-y.\left(x^{n-1}+y^{n-1}\right)\)
Rút gọn biểu thức: x^n-1 (x + y) - y (x^n-1 + y^n-1
xn – 1 (x + y) – y(xn – 1 + yn – 1) = xn+ xn – 1y – yxn – 1 - yn
= xn + xn – 1y - xn – 1y - yn
= xn – yn
Rút gọn các biểu thức sau:
a, M=90.10n-10n+2+10n+1
b, N=x(x+y)-y(x+y)
c, P=y(xn-1+yn-1)-xn-1(x+y)
Bài làm:
a) \(M=90.10^n-10^{n+2}+10^{n+1}\)
\(M=9.10.10^n-10^{n+2}+10^{n+1}\)
\(M=10^{n+1}\left(9-10+1\right)\)
\(M=10^{n+1}.0=0\)
b) \(N=x\left(x+y\right)-y\left(x+y\right)\)
\(N=\left(x-y\right)\left(x+y\right)\)
\(N=x^2-y^2\)
c) \(P=y\left(x^{n-1}+y^{n-1}\right)-x^{n-1}\left(x+y\right)\)
\(P=x^{n-1}y+y^n-x^n-x^{n-1}y\)
\(P=y^n-x^n\)
Học tốt!!!!
Rút gọn biểu thức :
a) \(x\left(x-y\right)+y\left(x-y\right)\)
b) \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
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.
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.
a)x(x-y)+y(x-y)
=x.x+x.(-y)+y.x+y.(-y)
=x2-xy+xy-y2
=x2-y2
rút gọn biểu thức
x(x-y)+y(x-y)
Xn-1(x+y)-y(xn-1+yn-1)
x(x-y)+y(x-y)
= x2-xy+xy-y2
= x2-y2
xn-1(x+y)-y(xn-1+yn-1)
= xn-1+1+xn-1y-xn-1y-y1+n-1
= xn-yn
1.x(x-y)+y(x-y)
=x^2-xy+xy-y^2
=x^2-y^2
2.x^n-1(x-y)-y(x^n-1+y^n-1)
=x^n-x^n-1y+x^n-1y-y^n
=x^n-y^n