Question

phân tích thành nhân tử

a) \(ab+b\sqrt{a}+\sqrt{a}+1\)

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

Answer 1

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

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

b) \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}=\left|x\right|\sqrt{x}-\left|y\right|\sqrt{y}+\left|x\right|\sqrt{y}+\left|y\right|\sqrt{x}\)

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

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

Answer 2

câu 1 sau rút gọn