Expand Using the Binomial Theorem (3x-7)^2

Problem

(3*x−7)^2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)^n where a=3*x b=−7 and n=2

2. Apply the Binomial Theorem formula, 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*(−7)^0+(2/1)(3*x)^1*(−7)^1+(2/2)(3*x)^0*(−7)^2)))

4. Evaluate the coefficients using the combination formula (n/k)=(n!)/(k!(n−k)!))

1⋅(3*x)^2⋅1+2⋅(3*x)⋅(−7)+1⋅1⋅(−7)^2

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

9*x^2−42*x+49

Final Answer

(3*x−7)^2=9*x^2−42*x+49

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