Question 792487
Factoring, using the special product {{{a^2-b^2=(a+b)(a-b)}}}:
{{{(2x+2y)^2 - (2x-2y)^2=((2x+2y)+(2x-2y))((2x+2y)-(2x-2y))=(2x+2y+2x-2y)(2x+2y-2x+2y)=(4x)(4y)=16xy}}}
 
Calculated a different way:
{{{(2x+2y)^2 - (2x-2y)^2=((2x)^2+2(2x)(2y)+(2y)^2)-((2x)^2-2(2x)(2y)+(2y)^2)}}}
At this point we can calculate that stuff, just to make the writing easier,and continue with
={{{(4x^2+8xy+4y^2)-(4x^2-8xy+4y^2)=4x^2+8xy+4y^2-4x^2+8xy-4y^2=8xy+8xy=16xy}}}
The other choice would be to continue with
={{{(2x)^2+2(2x)(2y)+(2y)^2-(2x)^2+2(2x)(2y)-(2y)^2=2(2x)(2y)+2(2x)(2y)=4(2x)(2y)=16xy}}}