Expand Using the Binomial Theorem (3x-1)^2

Problem

(3*x−1)^2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)^n where a=3*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)*b^k)

3. Write the expansion by substituting the values into the formula for k=0,1,2

(2/0)(3*x)^2*(−1)^0+(2/1)(3*x)^1*(−1)^1+(2/2)(3*x)^0*(−1)^2)))

4. Calculate the coefficients using the combination formula (n/k))

(2/0)=1)

(2/1)=2)

(2/2)=1)

5. Simplify each term by performing the exponentiation and multiplication.

1⋅9*x^2⋅1=9*x^2

2⋅3*x⋅(−1)=−6*x

1⋅1⋅1=1

6. Combine the terms to find the final expanded expression.

9*x^2−6*x+1

Final Answer

(3*x−1)^2=9*x^2−6*x+1

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