Discovering Patterns in the Difference of Squares Equation

[rocomath]

I'm looking for patterns and if you can add to things I noticed before working it out, that would be good :-]

1. $$(a+b+c)(a+b-c)=a^2+b^2+c^2+2ab$$

I noticed that b+c and b-c compensated for each other.

2. $$(a+b+c)(a-b-c)=a^2-b^2-c^2-2bc$$

a+b and a-b compensated for each other and the fact that it's b+c and -b-c, is the reason that it was -2bc?

3. $$(a+b-c)(a-b+c)=a^2-b^2-c^2+2bc$$

a+b and a-b compensated for each other, Now I figured from problem 2 that it would be 2bc again, but I didn't predict the sign correctly?

 

[rock.freak667]

Not sure I will be helpful here but all I can see is that

2. $$(a+b+c)(a-b-c)=a^2-b^2-c^2-2bc$$

a+b and a-b compensated for each other and the fact that it's b+c and -b-c, is the reason that it was -2bc?

$$(a+b+c)(a-b-c)==(a+(b+c))(a-(b+c))=(a)^2-(b+c)^2$$

and the same for the 3rd one.

for the first one:
$$(a+b+c)(a+b-c)((a+b)+c)((a+b)-c)$$

EDIT: oh wait...that is not what you were talking about...my bad

 

[rocomath]

EDIT: oh wait...that is not what you were talking about...my bad

Nope, lol. But I didn't even think about what you were doing (grouping then putting it in a more visible manner). Thanks, still helped!