Expand Using the Binomial Theorem (x+2)^3

Problem

(x+2)3

Solution

1. Identify the components of the binomial (a+b)n where a=x b=2 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 the expansion by substituting the values into the formula for each term from k=0 to k=3

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

4. Calculate the binomial coefficients using (n/k)=(n!)/(k!(n−k)!)) which gives 1, 3, 3, 1$.

1⋅x3⋅1+3⋅x2⋅2+3⋅x⋅4+1⋅1⋅8

5. Simplify each term by performing the multiplication.

x3+6*x2+12*x+8

Final Answer

(x+2)3=x3+6*x2+12*x+8

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