Square
A square can be taken over several terms.
Two terms
To solve a square with two terms you should calculate this term-by-term
(a + b)2
and that gives
(a + b) (a + b) = a·a + a·b + b·a + b·b
so
(a + b)2 = a2 + 2ab + b2
It's a binomial formula that is often used to simplify calculations. We check this with regular numbers
(2 + 3)2 = (2 + 3) (2 + 3) = 2·2 + 2·3 + 3·2 + 3·3 = 25
and this result is of course correct, as
(2 + 3)2 = (5)2 = 25
Three terms
A square with three terms is also calculated term-by-term from left to right
(a + b + c)2
which gives
(a + b + c) (a + b + c) = a a + a b + a c + b·a + b·b + b·c + c·a + c·b + c·c
so that
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
We check this with ordinary numbers
(2 + 3 + 4)2 = (2 + 3 + 4) (2 + 3 + 4) = 2·2 + 2·3 + 2·4 + 3·2 + 3·3 + 3·4 + 4·2 + 4·3 + 4·4 = 81
and that result is of course correct, because
(2 + 3 + 4)2 = (9)2 = 81
