Expand Using the Binomial Theorem (6x-5)^2

Problem

(6*x−5)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=6*x b=−5 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 terms of the expansion for n=2

(2/0)(6*x)2*(−5)0+(2/1)(6*x)1*(−5)1+(2/2)(6*x)0*(−5)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⋅36*x2⋅1=36*x2

2⋅6*x⋅(−5)=−60*x

1⋅1⋅25=25

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

36*x2−60*x+25

Final Answer

(6*x−5)2=36*x2−60*x+25

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