Expand Using the Binomial Theorem (6x-7)^2

Problem

(6*x−7)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=6*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)*bk)

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

(2/0)(6*x)2*(−7)0+(2/1)(6*x)1*(−7)1+(2/2)(6*x)0*(−7)2)))

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

1⋅(6*x)2⋅1+2⋅(6*x)⋅(−7)+1⋅1⋅(−7)2

5. Simplify each term by squaring the constants and variables.

36*x2−84*x+49

Final Answer

(6*x−7)2=36*x2−84*x+49

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