Expand Using the Binomial Theorem (x+1)^3

Problem

(x+1)3

Solution

1. Identify the parameters for the Binomial Theorem formula (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk) where a=x b=1 and n=3

2. Write the expansion as a sum of four terms using the binomial coefficients (3/0)) (3/1)) (3/2)) and (3/3))

(x+1)3=(3/0)x3*(1)0+(3/1)x2*(1)1+(3/2)x1*(1)2+(3/3)x0*(1)3))))

3. Calculate the binomial coefficients using Pascal's triangle or the formula (n/k)=(n!)/(k!(n−k)!)) which gives 1, 3, 3, 1$.

(x+1)3=1*(x3)*(1)+3*(x2)*(1)+3*(x)*(1)+1*(1)*(1)

4. Simplify each term by performing the multiplication.

(x+1)3=x3+3*x2+3*x+1

Final Answer

(x+1)3=x3+3*x2+3*x+1

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