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

Problem

(x+h)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=h and n=3

2. Write the expansion by applying the formula for each term from k=0 to k=3

(3/0)x3*h0+(3/1)x2*h1+(3/2)x1*h2+(3/3)x0*h3))))

3. Calculate the binomial coefficients (n/k)) using the formula (n!)/(k!(n−k)!) or Pascal's Triangle.

(3/0)=1)

(3/1)=3)

(3/2)=3)

(3/3)=1)

4. Substitute the coefficients back into the expression and simplify the powers.

1⋅x3⋅1+3⋅x2⋅h+3⋅x⋅h2+1⋅1⋅h3

5. Combine the terms to reach the final expanded form.

x3+3*x2*h+3*x*h2+h3

Final Answer

(x+h)3=x3+3*x2*h+3*x*h2+h3

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