Expand Using the Binomial Theorem (x-1)^3

Problem

(x−1)3

Solution

1. Identify the parameters for the Binomial Theorem (a+b)n where a=x b=−1 and n=3

2. Apply the formula for the expansion using the binomial coefficients (n/k))

(x−1)3=(3/0)x3*(−1)0+(3/1)x2*(−1)1+(3/2)x1*(−1)2+(3/3)x0*(−1)3))))

3. Calculate the binomial coefficients (3/0)=1) (3/1)=3) (3/2)=3) and (3/3)=1)

(x−1)3=1*(x3)*(1)+3*(x2)*(−1)+3*(x)*(1)+1*(1)*(−1)

4. Simplify each term by multiplying the coefficients and powers.

(x−1)3=x3−3*x2+3*x−1

Final Answer

(x−1)3=x3−3*x2+3*x−1

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