Question

phân tích thành nhân tử

a) A= \(xy+y\sqrt{x}+\sqrt{x}+1\left(x\ge0\right)\)

b) B= \(x-3\sqrt{xy}+2y\) \(\left(x\ge0;y\ge0\right)\)

c) C= \(2a-7\sqrt{ab}+5b\left(x\ge0;y\ge0\right)\)

Answer 1

a/ \(A=xy+y\sqrt{x}+\sqrt{x}+1\left(x\ge0\right)\)

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

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

b/ \(B=x-3\sqrt{xy}+2y\left(x\ge0;y\ge0\right)\)

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

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

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

c/\(C=2a-7\sqrt{ab}+5b\left(x\ge0;y\ge0\right)\)

\(=2a-2\sqrt{ab}-5\sqrt{ab}+5b\)

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

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

Answer 2