Question

My book says (A+B)^2=A^2+2AB+B^2. Can some some one show me why? When I work it out manually I get (A+B)^2=A^2+B^2... I do not see where the middle term comes from....

Answer 1

(A+B)(A+B)

if we call the first A+B C for the time being:
C(A+B)
what do you get ?

Answer 2

if you distribute the C

Answer 3

CA+CB

Answer 4

I think I get it now.. (A+B)^2 = (A+B)(A+B) = A^2+AB+BA+B^2 = A^2+2AB+B^2. Does the law (abc)^n = a^n b^n c^n not apply here because there are two terms inside the parenthesis?

Answer 5

the "exponent rule" only works for terms that are multiplied
for example
(abc)^2 means (abc)(abc) or (reordering) aa bb cc or a^2 b^2 c^2
on the other hand
(a+b)^2 means (a+b)(a+b)
unfortunately this turns out to be messier.

Answer 6

Thanks phi!