Expand Using the Binomial Theorem (x+8)^2

Problem

(x+8)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=8 and n=2

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

3. Write out the terms of the expansion for n=2

(2/0)x2*8+(2/1)x1*8+(2/2)x0*8)))

4. Calculate the binomial coefficients (2/0)=1) (2/1)=2) and (2/2)=1)

1⋅x2⋅1+2⋅x⋅8+1⋅1⋅64

5. Simplify each term by performing the multiplication.

x2+16*x+64

Final Answer

(x+8)2=x2+16*x+64

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