Expand Using the Binomial Theorem (5x-3)^2

Problem

(5*x−3)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=5*x b=−3 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 out the terms for k=0,1,2

(2/0)(5*x)2*(−3)0+(2/1)(5*x)1*(−3)1+(2/2)(5*x)0*(−3)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⋅25*x2⋅1=25*x2

2⋅5*x⋅(−3)=−30*x

1⋅1⋅9=9

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

Final Answer

(5*x−3)2=25*x2−30*x+9

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