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

Problem

(3*x+5)2

Solution

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

(2/0)(3*x)2*(5)0+(2/1)(3*x)1*(5)1+(2/2)(3*x)0*(5)2)))

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

1⋅(3*x)2⋅1+2⋅(3*x)⋅5+1⋅1⋅5

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

9*x2+30*x+25

Final Answer

(3*x+5)2=9*x2+30*x+25

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