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

Problem

(x+3)3

Solution

1. Identify the components of the binomial (a+b)n where a=x b=3 and n=3

2. Apply the Binomial Theorem formula, which states (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk)

3. Write out the terms for k=0,1,2,3

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

4. Calculate the binomial coefficients (n/k)) using the values 1, 3, 3, 1$ from Pascal's Triangle:

1⋅x3⋅1+3⋅x2⋅3+3⋅x⋅9+1⋅1⋅27

5. Simplify each term by performing the multiplication:

x3+9*x2+27*x+27

Final Answer

(x+3)3=x3+9*x2+27*x+27

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