Question

Phân tích thành nhân tử:

a) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\) (a,b,x,y \(\ge\) 0)

b) \(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\) (a,b\(\ge\) 0)

c) \(a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\) (a,b \(\ge\) 0)

d) \(\sqrt{x^2-25y^2}-\sqrt{x-5y}\left(x\ge5y\ge0\right)\)

Help meeeeeeee

Answer 1

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

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

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

b) \(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\)

\(=7\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)-\left(\sqrt{a}+\sqrt{b}\right)\)

\(=\left(\sqrt{a}+\sqrt{b}\right)\left(7\sqrt{b}-1\right)\)

c) \(a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\)

\(=\sqrt{a}\left(\sqrt{ab}+1\right)-\sqrt{b}\left(\sqrt{ab}+1\right)\)

\(=\left(\sqrt{ab}+1\right)\left(\sqrt{a}-\sqrt{b}\right)\)

d) \(\sqrt{x^2-25y^2}-\sqrt{x-5y}\)

\(=\sqrt{\left(x-5y\right)\left(x+5y\right)}-\sqrt{x-5y}\)

\(=\sqrt{x-5y}\left(\sqrt{x+5y}-1\right)\)