а) а+2√а = √а(√а+2)
б) √6-√18 = √6(1-√3)
в) х²-15 = (х-√15)(х+√15)
г) 4-4√х+х = (2-√х)²
д) 3х+6√(ху)+√х+2√у = (3х+√х) + (6√(ху)+2√у) =
√х(3√х+1) + 2√у(3√х+1) = (3√х+1)(√х+2√у)
c)
d)
e)
а) а+2√а = √а(√а+2)
б) √6-√18 = √6(1-√3)
в) х²-15 = (х-√15)(х+√15)
г) 4-4√х+х = (2-√х)²
д) 3х+6√(ху)+√х+2√у = (3х+√х) + (6√(ху)+2√у) =
√х(3√х+1) + 2√у(3√х+1) = (3√х+1)(√х+2√у)
c)![x^2 - 15 = x^2 - \sqrt{15^2}=x^2 - (\sqrt{15})^2=(x-\sqrt{15})(x+\sqrt{15})](/tpl/images/0085/9929/b6c8a.png)
d)![4-4\sqrt{x}+x= 2^2-2*2*\sqrt{x}+\sqrt{x}^2=\\ \\ =(2-\sqrt{x})^2](/tpl/images/0085/9929/49be2.png)
e)![3x+6\sqrt{xy}+\sqrt{x}+2\sqrt{y}=\\ \\ =3x+\sqrt{x}+6\sqrt{xy}+2\sqrt{y}=\\ \\ =\sqrt{x}(3\sqrt{x}+1)+2\sqrt{y}(3\sqrt{x}+1)=\\ \\ =(3\sqrt{x}+1)(\sqrt{x}+2\sqrt{y})](/tpl/images/0085/9929/df410.png)