How to calculate (a+b)^

[Daz dilu]

(a+b)^=(a+b)×(a+b)
=a×(a+b)+b×(a+b)
=a×a+a×b+b×a+b×b
=a^+ab+ab+b^
=a^+2ab+b^

 

[Otis]

Hello. Good work. Here's another way to write it.

(a+b)^2 = (a+b)(a+b)
(a+b)^2 = a(a+b) + b(a+b)
(a+b)^2 = a(a) + a(b) + b(a) + b(b)
(a+b)^2 = a^2 + ab + ab + b^2
(a+b)^2 = a^2 + 2ab + b^2



$\;$

 

[Harry_the_cat]

Are you interested in expanding other powers of $\displaystyle (a+b)$ eg $\displaystyle (a+b)^3, (a+b)^4$ etc? It is hard to tell from your title what index you are using.