Expand Using the Binomial Theorem (4x+5)^2

Problem

(4*x+5)^2

Solution

1. Identify the terms of the binomial (a+b)^n where a=4*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)*b^k)

3. Write the expansion using the combinations (2/0)) (2/1)) and (2/2))

(2/0)(4*x)^2*(5)^0+(2/1)(4*x)^1*(5)^1+(2/2)(4*x)^0*(5)^2)))

4. Calculate the coefficients and powers for each term.

1*(16*x^2)*(1)+2*(4*x)*(5)+1*(1)*(25)

5. Simplify the expression by performing the multiplication.

16*x^2+40*x+25

Final Answer

(4*x+5)^2=16*x^2+40*x+25

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