Question

Rút gọn biểu thức:

a) x ( x - y ) + y ( x - y )

b) x^n-1 ( x + y ) - y( x^n-1 + y^n-1 )

Answer 1

a) = (x - y)(x + y) = x² - y²

b) = xⁿ + x^{n - 1}y - yx^{n - 1} - yⁿ = xⁿ - yⁿ

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)`

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

 

Answer 3

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

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