Question

Phân tích đa thức thành nhân tử

a) ab+b√a+√a+1

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

Answer 1

a) \(ab+b\sqrt{a}+\sqrt{a}+1\)

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

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

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

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

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

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