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

1 Answer
Jun 14, 2018

Answer:

# (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 #