Tìm n thuộc N để có phép chia hết:
a) xn+2. yn+1 : x5. y6
b) (x + y)6n. (x - y)5 : (x + y)18. (x - y)n
c) (12x3y7 + 9x4y5 - 3x5y8) : 3xn+1. yn+3
d) (5xn-2. y7 - 8xn+2. y8) : 5x3. yn+1
Đề bài: Rút gọn hai biểu thức sau:
a) x(x-y)+y(x-y):
b) xn-1(x+y)-y(xn-1+yn-1).
a: ta có: \(x\left(x-y\right)+y\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)\)
\(=x^2-y^2\)
b: Ta có: \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
\(=x^n+x^{n-1}\cdot y-x^{n-1}\cdot y-y^n\)
\(=x^n-y^n\)
xn–1(x + y) – y(xn–1 + yn–1)
xn - 1(x + y) - y(xn - 1 + yn - 1)
= xn - x + y - yxn - y2 n - 1
rút gọn biểu thức
x(x-y)+y(x-y)
xn-1 (x+y)-y(xn-1+yn-1)
\(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
=\(x^n+x^{n-1}y-x^{n-1}y-y^n\)
=\(x^n-y^n\)
\(x\left(x-y\right)+y\left(x-y\right)\)
\(=x.x-x.y+y.x-y.y\)
\(=x^2-xy+yx-y^2\)
=\(x^2-y^2\)
x(x-y)+y(x-y)
= x.x+x.(-y)+y.x+y.(-y)
=x^2-xy+yx-y^2
=x^2-y^2
Rút gọn biểu thức: xn-1(x + y) – y(xn–1 + yn–1)
x(x – y) + y(x – y)
= x.x – x.y + y.x – y.y
= x2 – xy + xy – y2
= x2 – y2 + (xy – xy)
= x2 – y2
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
3xn - 2 . (xn+2- yn+2) + yn+2 . (3xn - 2 - yn - 2)
Tìm số tự nhiên n để X ⋮ Y biết X= 7 x2n -1-5x3;Y=5xn.
\(\dfrac{X}{Y}=\dfrac{7}{5}x^{n-1}-x^{3-n}\)
Để X chia hết cho Y thì n-1>=0 và 3-n>=0
=>1<=n<=3
=>\(n\in\left\{1;2;3\right\}\)
Chứng minh rằng x-y là ước của xm+yn thì x-y cũng là ước của xn+ym(Với x,y,m,n là số nguyên)
5(3xn+1-yn-1)-3(xn+1+2yn-1)+4(-xn+1+2yn-1)
\(5\left(3x^{n+1}-y^{n-1}\right)-3\left(x^{n+1}+2y^{n-1}\right)+4\left(-x^{n+1}+2y^{n-1}\right)\)
\(=15x^{n+1}-5y^{n-1}-3x^{n+1}-6y^{n-1}-4x^{n+1}+8y^{n-1}\)
\(=8x^{n+1}-3y^{n-1}\)