Question

Phân tích biểu thức sau về dạng nhân tử:

a) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)

b) \(x^2+x\sqrt{x}+\sqrt{x}+1\)

c) \(\sqrt{6.x}-x.2\sqrt{3}\)

Answer 1

a, \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)

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

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

b, \(x^2+x\sqrt{x}+\sqrt{x}+1\)

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

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

c, \(\sqrt{6x}-x2\sqrt{3}\)

\(=\sqrt{6x}-\sqrt{12x^2}\)

\(=\sqrt{6x}\left(1-\sqrt{2x}\right)\)