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

Problem

(x+h)2

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=2

2. Apply the formula by writing out the summation for k=0,1,2

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

3. Calculate the binomial coefficients (n/k)=(n!)/(k!(n−k)!)) which are (2/0)=1) (2/1)=2) and (2/2)=1)

1⋅x2⋅1+2⋅x⋅h+1⋅1⋅h2

4. Simplify the expression by multiplying the terms.

x2+2*x*h+h2

Final Answer

(x+h)2=x2+2*x*h+h2

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