How do you multiply #(x+1)^3#?

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Answer 1 · 2018-06-13T04:59:26

#(x+1)^3 = x^3+3x^2+3x+1#

The Binomial Theorem in one variable states that:

#(1+x)^n = sum_(k=0)^n ""^nC_k * x^k#

In this example #n=3#

#:. (1+x)^3 = ""^3C_0 x^0 + ""^3C_1 x^1 + ""^3C_2 x^2 + ""^3C_3 x^3#

#= 1 + 3x + (3xx2)/(2xx1) x^2 +x^3#

#= 1+3x+3x^2+x^3#

Rewriting terms in the order of the original question:

#(x+1)^3 = x^3+3x^2+3x+1#