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

=(x-y)-(căn x+căn y)

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

=(căn x+căn y)(căn x-căn y-1)

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

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

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

\(x\sqrt{y}-y\sqrt{x}=\sqrt{x^2}.\sqrt{y}-\sqrt{y^2}.\sqrt{x}=\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)

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

`x \sqrt{y} - y \sqrt{x}`

`= (\sqrt{x})^2 . \sqrt{y} - (\sqrt{y})^2 . \sqrt{x}`

`= \sqrt{x} . \sqrt{y} . (\sqrt{x} - \sqrt{y})`

`= \sqrt{xy} . (\sqrt{x} - \sqrt{y})`

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

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

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

= x(x^2 - 1) + y(x^2 - 1)

= ( x^2 -1)(x+y)

bạn có thể viết rõ hơn ko

x^4+x^2y^2+y^4

=x^4+2x^2y^2+y^4-x^2y^2

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

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

\(\sqrt{x}+\sqrt{y}+\sqrt{xy}+1\)

\(=\sqrt{x}+\sqrt{y}+\sqrt{x}.\sqrt{y}+1\)

\(=\sqrt{x}\left(\sqrt{y}+1\right)+\left(\sqrt{y}+1\right)\)

\(=\left(\sqrt{x}+1\right)\left(\sqrt{y}+1\right)\)

( căn x + 1 ) + ( căn y + căn xy )
( căn x + 1 ) + căn y.( căn x +  1)
( căn x +1 )(căn y + 1 )

Câu 1:

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

\(=\left(x-y+4\right)\cdot\left(x+y-4\right)\)

a: \(=x^2\left(x-2\right)\)

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

c: =(x-3)(x+2)