Question

Khai triển và rút gọn biểu thức (với x và y > 0):

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

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

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

Answer 1

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 ...

Answer 2

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

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

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