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

Problem

(x+2)4

Solution

1. Identify the components of the binomial (a+b)n where a=x b=2 and n=4

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 of the expansion using the combinations (4/k)) for k=0,1,2,3,4

(4/0)x4*2+(4/1)x3*2+(4/2)x2*2+(4/3)x1*2+(4/4)x0*2)))))

4. Calculate the binomial coefficients (4/0)=1) (4/1)=4) (4/2)=6) (4/3)=4) and (4/4)=1)

1⋅x4⋅1+4⋅x3⋅2+6⋅x2⋅4+4⋅x⋅8+1⋅1⋅16

5. Simplify each term by multiplying the coefficients and the powers of 2.

x4+8*x3+24*x2+32*x+16

Final Answer

(x+2)4=x4+8*x3+24*x2+32*x+16

Want more problems? Check here!