a,\(A=1+\sqrt{a}+\sqrt{b}+\sqrt{ab}=\left(1+\sqrt{a}\right)+\sqrt{b}\left(1+\sqrt{a}\right)=\left(1+\sqrt{a}\right)\left(1+\sqrt{b}\right)\)
b,\(B=\sqrt{ax}-\sqrt{by}-\sqrt{ay}+\sqrt{bx}=\sqrt{a}\left(\sqrt{x}-\sqrt{y}\right)+\sqrt{b}\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
c,\(C=\sqrt{x}+\sqrt{y}+\sqrt{x^2y}+\sqrt{xy^2}=\sqrt{x}\left(1+\sqrt{xy}\right)+\sqrt{y}\left(1+\sqrt{xy}\right)\)
\(=\left(1+\sqrt{xy}\right)\left(\sqrt{x}+\sqrt{y}\right)\)
d,\(D=x+2\sqrt{xy}+y-4=\left(\sqrt{x}+\sqrt{y}\right)^2-4=\left(\sqrt{x}+\sqrt{y}-2\right)\left(\sqrt{x}+\sqrt{y}+2\right)\)
e,\(E=x+\sqrt{x}-12=\left(x+4\sqrt{x}\right)-\left(3\sqrt{x}+12\right)=\sqrt{x}\left(\sqrt{x}+4\right)-3\left(\sqrt{x}+4\right)\)
\(=\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)
f,\(F=2a-5\sqrt{ab}+3b=\left(2a-2\sqrt{ab}\right)-\left(3\sqrt{ab}-3b\right)\)
\(=2\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)-3\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(2\sqrt{a}-3\sqrt{b}\right)\)
A=(1+\(\sqrt{a}\))+\(\sqrt{b}\)(1+\(\sqrt{a}\))=(1+\(\sqrt{a}\))(1+\(\sqrt{b}\))
B=\(\sqrt{a}\)(\(\sqrt{x}\)-\(\sqrt{y}\))+\(\sqrt{b}\)(\(\sqrt{x}\)-\(\sqrt{y}\))=(\(\sqrt{x}\)-\(\sqrt{y}\))(\(\sqrt{a}\)+\(\sqrt{b}\))
C=(\(\sqrt{x}\)+\(\sqrt{y}\))+\(\sqrt{xy}\)(\(\sqrt{x}\)+\(\sqrt{y}\))=(\(\sqrt{x}\)+\(\sqrt{y}\))(1+\(\sqrt{xy}\))
D=(\(\sqrt{x}\)+\(\sqrt{y}\))\(^2\)-2=(\(\sqrt{x}\)+\(\sqrt{y}\)-2)(\(\sqrt{x}\)+\(\sqrt{y}\)+2)
E=x-\(3\sqrt{x}\)+\(4\sqrt{x}\)-12=\(\sqrt{x}\)(\(\sqrt{x}\)-3)+4(\(\sqrt{x}\)-3)=(\(\sqrt{x}\)-3)(\(\sqrt{x}\)+4)
F=2a-2\(\sqrt{ab}\)-3\(\sqrt{ab}\)+3b=2\(\sqrt{a}\)(\(\sqrt{a}\)-\(\sqrt{b}\))-3\(\sqrt{b}\)(\(\sqrt{a}\)-\(\sqrt{b}\))=
(\(\sqrt{a}\)-\(\sqrt{b}\))(2\(\sqrt{a}\)-\(3\sqrt{b}\))
