Question

Phân tích đa thức thành nhân tử:

a) \(\sqrt{a^2-b^2}\) - \(\sqrt{a^3+b^3}\)

b) x - \(3\sqrt{x}\) - 18

c) \(x\sqrt{x}\) + 4x - \(12\sqrt{x}\) - 27

Answer 1

a/ \(=\sqrt{\left(a-b\right)\left(a+b\right)}-\sqrt{\left(a+b\right)\left(a^2-ab+b^2\right)}\)

\(=\sqrt{a+b}\left(\sqrt{a-b}-\sqrt{a^2-ab+b^2}\right)\)

b/ \(=x-3\sqrt{x}+\frac{9}{4}-\frac{81}{4}=\left(\sqrt{x}-\frac{3}{2}\right)^2-\frac{81}{4}\)

\(=\left(\sqrt{x}-\frac{3}{2}-\frac{9}{2}\right)\left(\sqrt{x}-\frac{3}{2}+\frac{9}{2}\right)=\left(\sqrt{x}-6\right)\left(\sqrt{x}+3\right)\)

c/ \(=\left(\sqrt{x}\right)^3-3^3+4\sqrt{x}\left(\sqrt{x}-3\right)\)

\(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)+4\sqrt{x}\left(\sqrt{x}-3\right)=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9+4\sqrt{x}\right)\)

\(=\left(\sqrt{x}-3\right)\left(x+7\sqrt{x}+9\right)\)