Expand Using the Binomial Theorem (x-1)^2

Problem

(x−1)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=−1 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 the terms of the expansion using the combinations (2/0)) (2/1)) and (2/2))

(x−1)2=(2/0)x2*(−1)0+(2/1)x1*(−1)1+(2/2)x0*(−1)2)))

4. Calculate the coefficients and simplify the powers.

(x−1)2=1⋅x2⋅1+2⋅x⋅(−1)+1⋅1⋅1

5. Simplify the expression by performing the multiplication.

(x−1)2=x2−2*x+1

Final Answer

(x−1)2=x2−2*x+1

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