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

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

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

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

a) \(xy-y\sqrt{x}+\sqrt{x}-1\)

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

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

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

\(=\left(\sqrt{ax}-\sqrt{ay}\right)+\left(-\sqrt{by}+\sqrt{bx}\right)\)

\(=\sqrt{a}.\left(\sqrt{x}-\sqrt{y}\right)+\sqrt{b}.\left(\sqrt{x}-\sqrt{y}\right)\)

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

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

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

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

b, \(x^2+x\sqrt{x}+\sqrt{x}+1\)

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

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

c, \(\sqrt{6x}-x2\sqrt{3}\)

\(=\sqrt{6x}-\sqrt{12x^2}\)

\(=\sqrt{6x}\left(1-\sqrt{2x}\right)\)

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

b,\(x\sqrt{x}+\sqrt{x}-x-1\)

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

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

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

c,\(\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)=\(\sqrt{a}\left(\sqrt{b}+2\right)\)+\(3\left(\sqrt{b}+2\right)\)

=\(\left(\sqrt{b}+2\right)\left(3+\sqrt{a}\right)\)

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

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

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

a/ \(=\sqrt{a}\left(\sqrt{x}-\sqrt{y}\right)-\sqrt{b}\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{a}-\sqrt{b}\right)\)

b/ \(=\sqrt{\left(a-b\right)\left(a+b\right)}-\sqrt{\left(a+b\right)\left(a^2-ab+b^2\right)}\)

\(=\sqrt{a+b}\left(\sqrt{\left(a-b\right)\left(a^2-ab+b^2\right)}\right)\)

c/ \(=\left(\sqrt{x}-\frac{3}{2}\right)^2-\frac{81}{4}=\left(\sqrt{x}-\frac{3}{2}-\frac{9}{2}\right)\left(\sqrt{x}-\frac{3}{2}+\frac{9}{2}\right)=\left(\sqrt{x}-6\right)\left(\sqrt{x}+3\right)\)

\(a.\sqrt{ax}+\sqrt{by}-\sqrt{ay}-\sqrt{bx}\\ =\left(\sqrt{ax}-\sqrt{ay}\right)-\left(\sqrt{bx}-\sqrt{by}\right)\\ =\sqrt{a}\left(\sqrt{x}-\sqrt{y}\right)-\sqrt{b}\left(\sqrt{x}-\sqrt{y}\right)\\ =\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{x}-\sqrt{y}\right)\)

\(b.\sqrt{a^2-b^2}-\sqrt{a^3+b^3}\\ =\sqrt{\left(a+b\right)\left(a-b\right)}-\sqrt{\left(a+b\right)\left(a^2-ab+b^2\right)}\\ =\sqrt{a+b}\left(\sqrt{a-b}-\sqrt{a^2-ab+b^2}\right)\)

\(c.x-3\sqrt{x}-18=x-6\sqrt{x}+3\sqrt{x}-18\\ =\sqrt{x}\left(\sqrt{x}-6\right)+3\left(\sqrt{x}-6\right)\\ =\left(\sqrt{x}+3\right)\left(\sqrt{x}-6\right)\)

\(d.x\sqrt{x}+4x-12\sqrt{x}-27=\left(\sqrt{x^3}-27\right)+\left(4x-12\sqrt{x}\right)\\ =\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)+4\sqrt{x}\left(\sqrt{x}-3\right)\\ =\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9+4\sqrt{x}\right)\\ =\left(\sqrt{x}-3\right)\left(x+7\sqrt{x}+9\right)\)

(có gì sai mong mọi người góp ý)

d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)