How do you multiply (a+b)(a+b)(a+b)(a+b)(a+b)(a+b)?

1 Answer
Jun 14, 2018

(a+b)(a+b)(a+b) = a^3 + 3a^2b + 3ab^2 + b^3 (a+b)(a+b)(a+b)=a3+3a2b+3ab2+b3

Explanation:

We seek an expansion of:

P(x) = (a+b)(a+b)(a+b) P(x)=(a+b)(a+b)(a+b)

So, we can write:

P(x) = (a+b)^3 P(x)=(a+b)3

Then, using the Binomial Theorem:

P(x) = ( (3),(0) ) a^3b^0 + ( (3),(1) ) a^2b^1 + ( (3),(2) ) a^1b^2 + ( (3),(3) ) a^0b^3

\ \ \ \ \ \ \ \ = a^3 + 3a^2b + 3ab^2 + b^3