Expand Using the Binomial Theorem (x-4)^3

Problem

(x−4)3

Solution

1. Identify the parameters for the Binomial Theorem formula (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk) where a=x b=−4 and n=3

2. Write the expansion using the binomial coefficients for n=3 which are (3/0)) (3/1)) (3/2)) and (3/3))

(x−4)3=(3/0)x3*(−4)0+(3/1)x2*(−4)1+(3/2)x1*(−4)2+(3/3)x0*(−4)3))))

3. Calculate the binomial coefficients and the powers of −4

(x−4)3=1⋅x3⋅1+3⋅x2⋅(−4)+3⋅x⋅16+1⋅1⋅(−64)

4. Simplify each term by multiplying the constants.

(x−4)3=x3−12*x2+48*x−64

Final Answer

(x−4)3=x3−12*x2+48*x−64

Want more problems? Check here!