I'm assuming you want to simplify the expression?
Original expression
(a + b + c)2 - (a + b - c)2
Expand exponents
(a + b + c) * (a + b + c) - (a + b - c) * (a + b - c)
Multiply out the brackets (essentially FOIL)
(a2 + ab + ac + ba + b2 + bc + ca + cb + c2) - (a2 + ab - ac + ba + b2 - bc - ca - cb + c2)
Substitute in the minus sign (second brackets set) and remove all the brackets
a2 + ab + ac + ba + b2 + bc + ca + cb + c2 - a2 - ab + ac - ba - b2 + bc + ca + cb -c2
Simplify like terms (and cancel out the ones that aer opposite {ex. +2ab and -2ab})
a2 + 2ab + 2ac + b2 + 2bc + c2 - a2 - 2ab + 2ac - b2 + 2bc - c2
2ac + 2bc + 2ac + 2bc
4ac + 4bc
Pull out the 4 and the c as they are constant in all remaining terms
4c(a+b)
Breathe a breath of relief :)
