Question

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

\(b,\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)

\(c,a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}\)

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Answer 1

\(a,=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\\ =\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\\ b,=\sqrt{x}\left(\sqrt{a}+\sqrt{b}\right)-\sqrt{y}\left(\sqrt{a}+\sqrt{b}\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{a}+\sqrt{b}\right)\\ c,=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)\\ =\left(\sqrt{a}+2\sqrt{b}\right)\left(\sqrt{a}+1\right)\)