Expand Using the Binomial Theorem (x-9)^2

Problem

(x−9)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=−9 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*(−9)0+(2/1)x1*(−9)1+(2/2)x0*(−9)2)))

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

5. Simplify each term in the expression:

1⋅x2⋅1+2⋅x⋅(−9)+1⋅1⋅81

6. Combine the simplified terms to find the final expanded form:

x2−18*x+81

Final Answer

(x−9)2=x2−18*x+81

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