Question

Phân tích đa thức thành nhân tử

a) 7.\(\sqrt{AB}\)+ 7B -\(\sqrt{A}\)- \(\sqrt{B}\) (  Với A>= 0,  B>=0)b) a \(\sqrt{b}\)- b\(\sqrt{a}\)+ \(\sqrt{a}\)-\(\sqrt{b}\) (  Với a>= 0,  b>=0)\(\sqrt{x^2-25y^2}\)- \(\sqrt{x-5y}\) (  Với x >=  5y >= 0 )

Answer 1

\(a,7\sqrt{AB}+7B-\sqrt{A}-\sqrt{B}\)(  Với A>= 0,  B>=0)

\(=\left(7\sqrt{AB}-\sqrt{A}\right)+\left(7B-\sqrt{B}\right)\)

\(=7\sqrt{A}\left(\sqrt{B}-1\right)+7\sqrt{B}\left(\sqrt{B}-1\right)\)

\(=\left(\sqrt{B}-1\right)\left(7\sqrt{A}+7\sqrt{B}\right)\)

\(=7\left(\sqrt{B}-1\right)\left(\sqrt{A}+\sqrt{B}\right)\)

Answer 2

\(b,a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\)Với a>= 0,  b>=0)

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

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

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

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

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

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