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

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

\(y-2x\sqrt{y}-3x\sqrt{y}+6x^2=\sqrt{y}\left(\sqrt{y}-2x\right)-3x\left(\sqrt{y}-2x\right)=\left(\sqrt{y}-3x\right)\left(\sqrt{y}-2x\right)\)

\(\sqrt{x}=a;a>0\Leftrightarrow A=a^3-3a^2+4a-2\)

\(\Leftrightarrow A=\left(a^3-3a^2+3a-1\right)+\left(a-1\right)\)

\(\Leftrightarrow A=\left(a-1\right)^3+\left(a-1\right)\)

\(A=\left(a-1\right)\left[\left(a-1\right)^2+1\right]\)

\(A=\left(\sqrt{x}-1\right)\left(x-2\sqrt{x}+2\right)\)

\(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\) =\(7\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)-\left(\sqrt{a}+\sqrt{b}\right)\)                                                                                                                      =\(\left(\sqrt{a}+\sqrt{b}\right)\left(7\sqrt{b}-1\right)\)

\(x+\sqrt{x}+2\sqrt{x}+2\)

= \(\sqrt{x}\left(\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)

= \(\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)\)

\(2x-2\sqrt{x}+3\sqrt{x}-3\)

= \(2\sqrt{x}\left(\sqrt{x}-1\right)+3\left(\sqrt{x}-1\right)\)

= \(\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)\)

\(a,\left(3x+1\right)^2-\left(x+1\right)^2\)

\(=\left(3x+1-x-1\right)\left(3x+1+x+1\right)\)

\(=2x\left(4x+2\right)\)

\(=4x\left(2x+1\right)\)

\(b,6x-6y-x^2+xy\)

\(=\left(6x-6y\right)-\left(x^2-xy\right)\)

\(=6\left(x-y\right)-x\left(x-y\right)\)

\(=\left(x-y\right)\left(6-x\right)\)