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

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

\(=x^2-y^2\)

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

= x² - xy + xy + y²

= x² + y²

x.(x-y) + y.(x+y)

= x² - xy + yx + y²

= x² + y²

ta có: x(x-y)+y(x+y)

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

=x^2-y^2

x ( x - y ) + y ( y - x )
= x ( x - y ) - y ( x - y )

= ( x - y ) ( x - y )

= ( x - y )²

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

(=)\(x^2+y^2\)

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

\(=x\left(x-y\right)-y\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y\right)\)

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

Lời giải:

a) ĐK: $x\geq 0; y\geq 0; x\neq y$

\(A=\left[\frac{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}{\sqrt{x}-\sqrt{y}}-\frac{(\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y)}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}\right]:\frac{x-\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\)

\(=\left(\sqrt{x}+\sqrt{y}-\frac{x+\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\right).\frac{\sqrt{x}+\sqrt{y}}{x-\sqrt{xy}+y}\)

\(=\frac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}.\frac{\sqrt{x}+\sqrt{y}}{x-\sqrt{xy}+y}=\frac{\sqrt{xy}}{x-\sqrt{xy}+y}\)

b) \(1-A=\frac{(\sqrt{x}-\sqrt{y})^2}{x-\sqrt{xy}+y}>0\) với mọi $x\neq y; x,y\geq 0$

$\Rightarrow A< 1$

(x + y + z)² - 2(x + y + z)(x + y) + (x + y)²

= (x + y + z + x +y)²

= (2x + 2y + z)²

Chúc bạn học tốt !

\(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\)

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

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

\(=z^2\)

Áp dụng BĐT: \(\left(a-b\right)^2=a^2-2ab+b^2\)

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

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

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

giup mik nha tí 30p nữa mình on cam on mn

Hình như ghi sai đề hay sao í

làm lại đề nha x^2?9z-y)(x-z)+y^2/(x-y)(z-y)+z^2/(y-z)(x-z)

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

Theo mình là :

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

                                        = (x-y)(x+y) + x²+y² + x² - 2xy + y²

                                        = x² - y² + x² +y² + (x-y)²

Hãy nhìn kĩ đây là hằng đẳng thức đó
   (x + y)² + 2(x - y)(x + y) + (x - y)²
= (x + y + x - y)²
= (2x)²
= 4x²