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

1 Answer
Jun 13, 2018

(x+1)^3 = x^3+3x^2+3x+1(x+1)3=x3+3x2+3x+1

Explanation:

The Binomial Theorem in one variable states that:

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

In this example n=3n=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