\(a,\left(4\sqrt{x}-\sqrt{2x}\right)\left(\sqrt{x}-\sqrt{2x}\right)=4x-4\sqrt{2}x-\sqrt{2}x+2x=6x-5\sqrt{2}x=\left(6-5\sqrt{2}\right)x\)

\(b,\left(2\sqrt{x}+\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)=6x-4\sqrt{xy}+3\sqrt{xy}-2y=6x-4\sqrt{xy}-2y\)

a/ 6x

b/ 6x-2y-\(\sqrt{xy}\)

a)\(\left(1-\sqrt{x}\right)\left(1+\sqrt{x}+x\right)=1-\sqrt{x^3}\)

b) \(\left(\sqrt{x}+2\right)\left(x-2\sqrt{x}+4\right)=\sqrt{x^3}+8\)

c)\(\left(\sqrt{x}-\sqrt{y}\right)\left(x+y+\sqrt{xy}\right)=\sqrt{x^3}-\sqrt{y^3}\)

d)\(\left(x+\sqrt{y}\right)\left(x^2+y-x\sqrt{y}\right)=x^3+\sqrt{y^3}\)

Giải:

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

\(=\left(\sqrt{x}\right)^3-1\)

Vậy ...

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

\(=\left(\sqrt{x}\right)^3+\left(\sqrt{y}\right)^3\)

Vậy ...

c) \(\left(2\sqrt{x}+\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)\)

\(=6x+3\sqrt{xy}-4\sqrt{xy}-2y\)

\(=6x-\sqrt{xy}-2y\)

Vậy ...

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

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

\(c.\left(2\sqrt{x}+\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)=6x-\sqrt{xy}-2y\)

a) \(\sqrt{36\left(x-5\right)^2}\left(x\ge5\right)=6\left|x-5\right|=6\left(x-5\right)=6x-30\)

b) \(\sqrt{\dfrac{1}{4}\left(1-x\right)^2}\left(x>1\right)=\dfrac{1}{2}\left|1-x\right|=\dfrac{1}{2}\left(x-1\right)=\dfrac{1}{2}x-\dfrac{1}{2}\)

c) \(\sqrt{x^2\left(2x-4\right)^2}\left(x\ge2\right)=\left|x\left(2x-4\right)\right|=x\left(2x-4\right)=2x^2-4x\)

d) \(\dfrac{1}{x}\sqrt{x^2\left(1+x\right)^2}\left(x< -1\right)=\dfrac{1}{x}\left|x\left(1+x\right)\right|=\dfrac{1}{x}x\left(1+x\right)=1+x\)

B