\(\left(x+y-1\right)\left(x+y+1\right)=x^2+xy-x+xy+y^2-y+x+y-1\\ =x^2+\left(xy+xy\right)+\left(-x+x\right)+y^2+\left(-y+y\right)-1\\ =x^2+2xy+y^2-1\\ =>B\)

a.

(x^2 + y^2 - 2xy) + (x^2 + y^2 + 2xy)

= x^2 + y^2 - 2xy + x^2 + y^2 + 2xy

= (x^2 + x^2) + (y^2 + y^2) + (2xy - 2xy)

= 2x^2 + 2y^2

b.

(x^2 + y^2 - 2xy) - (x^2 + y^2 + 2xy)

= x^2 + y^2 - 2xy - x^2 - y^2 - 2xy

= (x^2 - x^2) + (y^2 - y^2) - (2xy + 2xy)

= -4xy

\(\left(x+y-2xy\right)\left(x+y+2xy\right)\)

\(=\left(x+y\right)^2-4x^2y^2\)

\(=x^2+2xy+y^2-4x^2y^2\)

\(\left(x+y-2xy\right)\left(x+y+2y\right)\)

\(=\left[\left(x+y\right)-2xy\right]\left[\left(x+y\right)+2xy\right]\)

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

\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)

\(\dfrac{x}{x^2+2xy+y^2}+\dfrac{2y}{x+y}+\dfrac{y}{x^2+2xy+y^2}\)

\(=\dfrac{x+y}{\left(x+y\right)^2}+\dfrac{2y}{x+y}\)

\(=\dfrac{1}{x+y}+\dfrac{2y}{x+y}=\dfrac{2y+1}{x+y}\)

a) \(\dfrac{2x^2-2xy}{x^2+x-xy-y}\) \(\left(x\ne y;x\ne-1\right)\)

\(=\dfrac{2x\left(x-y\right)}{x\left(x+1\right)-y\left(x+1\right)}\)

\(=\dfrac{2x\left(x-y\right)}{\left(x-y\right)\left(x+1\right)}\)

\(=\dfrac{2x}{x+1}\)

b) \(\dfrac{x^2+y^2-z^2+2xy}{x^2-y^2+z^2+2xz}\)

\(=\dfrac{\left(x^2+2xy+y^2\right)-z^2}{\left(x^2+2xz+z^2\right)-y^2}\)

\(=\dfrac{\left(x+y\right)^2-z^2}{\left(x+z\right)^2-y^2}\)

\(=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{\left(x-y+z\right)\left(x+y+z\right)}\)

\(=\dfrac{x+y-z}{x-y+z}\)

giúp tui với mấy bạn ơi

A

Uả bạn đang kiểm tra hay sao mà gấp thế?

\(\left(x^3+3x^2y+3xy^2+y^3-z^3\right):\left(x+y-z\right)\\ =\left[\left(x+y\right)^3-z^3\right]:\left(x+y-z\right)\\ =\left(x+y-z\right)\left[\left(x+y\right)^2+z\left(x+y\right)+z^2\right]:\left(x+y-z\right)\\ =x^2+2xy+y^2+xz+yz+z^2\)

Vậy chọn A