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

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Answer 1 · 2018-06-28T23:18:23

#(a+b)^3#

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

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

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

Answer 2 · 2018-06-28T23:20:51

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

#(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!