Question

Phân tích thành nhân tử:

a)  \(xy-y\sqrt{x}+\sqrt{x}-1\)

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

 

Answer 1

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

Answer 2

a) \(xy-y\sqrt{x}+\sqrt{x}-1\)

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

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

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

\(=\left(\sqrt{ax}-\sqrt{ay}\right)+\left(-\sqrt{by}+\sqrt{bx}\right)\)

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

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