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What is the formula for #(a+b)^3#?

1 Answer

Massimiliano · David Y.

Feb 3, 2015

The answer is: #(a+b)^3=a^3+3a^2b+3ab^2+b^3#.

It's easy to prove:

#(a+b)^3=#
#=(a+b)(a+b)(a+b)=#
#=(a^2+ab+ab+b^2)(a+b)=#
#=(a^2+2ab+b^2)(a+b)=#
#=a^3+a^2b+2a^2b+2ab^2+ab^2+b^3=#
#=a^3+3a^2b+3ab^2+b^3#.

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