[latex]a)\\(x-5y)(x+5y)=x^2-(5y)^2=x^2-25y^2\\b)\\(3x^2-1)(3x^2+1)=(3x^2)^2-1^2=9x^4-1[/latex]
[latex]c)\\(3,5a-0,5b)(3,5a+0,5b)=(3,5a)^2 -(0,5b)^2=12,25a^2-0,25b^2\\d)\\(5+2x)(2x-5)=(2x+5 )(2x-5)=(2x)^2-5^2=4x^2-25[/latex]
[latex]e)\\(3x+sqrt{3})( -sqrt{3}+3x)= (3x+sqrt{3})(3x -sqrt{3} )=(3x)^2 -(sqrt{3} )^2=9x^2-3\\f)\\( sqrt{6}k^2-sqrt{8}m^2)( sqrt{6}k^2+sqrt{8}m^2)= ( sqrt{6}k^2)^2-(sqrt{8}m^2)^2=6k^4-8m^4[/latex]
[latex]1)\\( sqrt{3}k +sqrt{6}m )^2= ( sqrt{3}k)^2+2* sqrt{3}k *sqrt{6}m +(sqrt{6}m )^2=3k^2+2sqrt{18}km+6m^2=\\=3k^2+2sqrt{9*2}km+6m^2=3k^2+6sqrt{ 2}km+6m^2[/latex]
[latex]2)\\(sqrt{2}k+0,5m)^2 = (sqrt{2}k)^2+2*sqrt{2}k*0,5m+(0,5m)^2 =2k^2+sqrt{2}km +0,25m^2[/latex]