Question

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))`

Answer 1

`a)x(x-y)+y(x-y)=(x-y)(x+y)=x^2-y^2`

`b)x^[n-1] (x+y)-y(x^[n-1]+y^[n-1])`

`=x^[n-1].x+x^[n-1] .y-y.x^[n-1]-y.y^[n-1]`

`=x^[n-1+1]-y^[1+n-1]`

`=x^n -y^n`

Answer 2

a) \(x\left(x-y\right)+y\left(x-y\right)=\left(x+y\right)\left(x-y\right)=x^2-y^2\)

b) \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)=x^n+x^{n-1}y-x^{n-1}y-y^n=x^n-y^n\)