\(\left(x+y\right)^2+\left(x-y\right)^2+\left(x-y\right)\left(x+y\right)-3x^2\)

\(=\left(x^2+2xy+y^2\right)+\left(x^2-2xy+y^2\right)+\left(x^2-y^2\right)-3x^2\)

\(=x^2+2xy+y^2+x^2-2xy+y^2+x^2-y^2-3x^2\)

\(=3x^2+y^2-3x^2\)

\(=y^2\)

1: \(C=\left(x-\dfrac{4xy}{x+y}+y\right):\left(\dfrac{x}{x+y}+\dfrac{y}{y-x}+\dfrac{2xy}{x^2-y^2}\right)\)

\(=\dfrac{\left(x+y\right)^2-4xy}{x+y}:\left(\dfrac{x}{x+y}-\dfrac{y}{x-y}+\dfrac{2xy}{\left(x-y\right)\left(x+y\right)}\right)\)

\(=\dfrac{x^2+2xy+y^2-4xy}{x+y}:\dfrac{x\left(x-y\right)-y\left(x+y\right)+2xy}{\left(x+y\right)\left(x-y\right)}\)

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

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

2: \(\left(x^2-y^2\right)\cdot C=-8\)

=>\(\left(x-y\right)\left(x+y\right)\cdot\dfrac{\left(x-y\right)^2}{x+y}=-8\)

=>\(\left(x-y\right)^3=-8\)

=>x-y=-2

=>x=y-2

\(M=x^2\left(x+1\right)-y^2\left(y-1\right)-3xy\left(x-y+1\right)+xy\)

\(=\left(y-2\right)^2\left(y-2+1\right)-y^2\left(y-1\right)-3xy\left(-2+1\right)+xy\)

\(=\left(y-1\right)\left[\left(y-2\right)^2-y^2\right]+3xy+xy\)

\(=\left(y-1\right)\left(-4y+4\right)+4xy\)

\(=-4\left(y-1\right)^2+4y\left(y-2\right)\)

\(=-4y^2+8y-4+4y^2-8y\)
=-4

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

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

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

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

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

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

\(=-z^2\)

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

\(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)

\(=2x^2-4xy+\dfrac{15}{4}y^2\)

b: \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)

\(=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)

\(=2x^2+2x+13-2x^2+2\)

=2x+15

a) \(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2=2x^2-4xy+\dfrac{15}{4}y^2\)

b) \(=x^2-4x+4+x^2+6x+9-2x^2+2\)

\(=2x+15\)

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

= \(x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)

= \(2x^2-4xy+\dfrac{15}{4}y^2\)

b; \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)

= \(x^2-4x+4+x^2+6x+9-2x^2+2\)

= \(2x+15\)

ngu the

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

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

\(=x^2+y^2+z^2-2xy-2yz+2xz+z^2-2yz+y^2+2xy-2y^2+2yz-2xz+2yz-2z^2\)

\(=x^2\)

Ta có: (x - y + z)² +2(x - y + z)( y - z) +( z- y)² = (x - y + z+ z- y)² =(x - 2y + 2z)²

tra loi nhanh di ae

$\left(x^{\sqrt{2}}y\right)^{\sqrt{2}} = x^{\sqrt{2} \cdot \sqrt{2}}y^{\sqrt{2}} = x^2y^{\sqrt{2}}$

$x^2y^{\sqrt{2}} \cdot 9y^{-\sqrt{2}} = 9x^2y^{\sqrt{2}}y^{-\sqrt{2}} = 9x^2$

Ta có \(x-y=1\)

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

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

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

\(A=x^8-y^8\)

= \(-\left[\left(x-y\right)\left(x^2-y^2\right)\left(x^4-y^4\right)\left(x^8-y^8\right)\left(x^{16}-y^{16}\right)\right]\)

= \(-\left[\left(x-y\right)\left(x-y\right)^2\left(x-y\right)^4\left(x-y\right)^8\left(x-y\right)^{16}\right]\)

= \(-\left(1\cdot1^2\cdot1^4\cdot1^8\cdot1^{16}\right)\)

= -1

=(x^2-y^2)(X^2+y^2)(X^4+y^4)(x^8+y^8)

=(x^4-y^4)(x^4+y^4)(x^8+y^8)

=(x^8-y^8)(x^8+y^8)

=x^16 - y^ 16

IF you can , give my answer a k

Bạn áp dụng hằng đẳng thức x² - y² = (x-y)(x+y) 

\(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)

\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)

\(=\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)

\(=\left(x^8-y^8\right)\left(x^8+y^8\right)=x^{16}-y^{16}\)

(x-y)(x+y)(x²+y²)(x⁴+y⁴)(x⁸+y⁸)

= (x²-y²)(x²+y²)(x⁴+y⁴)(x⁸+y⁸)

= (x⁴-y⁴)(x⁴+y⁴)(x⁸+y⁸)

= (x⁸-y⁸)(x⁸+y⁸)

= (x¹⁶-y¹⁶)

#Ttt

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