Question

Phân tích đa thức thành nhân tử

a, \(3\sqrt{2}-2\sqrt{3}+\sqrt{6}\)

b, \(2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3\)

c,\(\sqrt{8}-\sqrt{5}-2+\sqrt{10}\)

d,\(a\sqrt{b}+b\sqrt{a}\)

e,\(ab+b\sqrt{a}-\sqrt{a}-1\)

f,\(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\)

Answer 1

a)

\(3\sqrt{2}-2\sqrt{3}+6\)

\(=\sqrt{6}\left(\sqrt{3}-\sqrt{2}+\sqrt{6}\right)\)

b)

\(2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3\)

\(=2\sqrt{5}\left(\sqrt{3}-\sqrt{2}\right)-\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)\)

\(=\left(\sqrt{3}-\sqrt{2}\right)\left(2\sqrt{5}-\sqrt{3}\right)\)

c)

\(\sqrt{8}-\sqrt{5}-2+\sqrt{10}\)

\(=2\left(\sqrt{2}-1\right)+\sqrt{5}\left(\sqrt{2}-1\right)\)

\(=\left(\sqrt{2}-1\right)\left(2+\sqrt{5}\right)\)

d)

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

e)

\(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\)

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

\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)