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)*bk)

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*x2)*(1)+2*(4*x)*(5)+1*(1)*(25)

5. Simplify the expression by performing the multiplication.

16*x2+40*x+25

Final Answer

(4*x+5)2=16*x2+40*x+25

Want more problems? Check here!