How do you multiply #(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 #
Explanation:
We seek an expansion of:
# P(x) = (a+b)(a+b)(a+b) #
So, we can write:
# 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 #
