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

Problem

(3*x−2)2

Solution

1. Identify the terms of the binomial (a+b)n where a=3*x b=−2 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 expansion by substituting the values into the formula for k=0,1,2

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

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

1⋅(9*x2)⋅1+2⋅(3*x)⋅(−2)+1⋅1⋅4

5. Simplify each term to find the final polynomial.

9*x2−12*x+4

Final Answer

(3*x−2)2=9*x2−12*x+4

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