How do you simplify #(a+b)^3#?

2 Answers

#(a+b)^3#

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

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

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

Jun 28, 2018

Answer:

#a^3+3a^2b+3ab^2+b^3#

Explanation:

#(a+b)^3# is the same as #(a+b)^2(a+b)#, so if we write it in this way, it becomes a much easier problem to solve.

#(a+b)^2# is the same as #(a+b)(a+b)#, and if we distribute the #a# and #b# to both terms, we'll get

#a^2+2ab+b^2#

We now have

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

Again, we can distribute the #a# and #b# to all terms to get

#a^3+2a^2b+ab^2+a^2b+2ab^2+b^3#

This simplifies to

#a^3+3a^2b+3ab^2+b^3#

Hope this helps!