Expand Using the Binomial Theorem (x-2)^3

Problem

(x−2)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=−2 and n=3

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

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

3. Calculate the binomial coefficients, which are 1, 3, 3, 1b*a*s(e)*d(o)*n*P*a*s(c)*a*l′*s(T)*r*i*a*n*g*l*e*o*r*t*h*e*ƒ*o*r*m*u*l*afrac{n!}{k!(n-k)!}$.

1⋅x3⋅1+3⋅x2⋅(−2)+3⋅x⋅4+1⋅1⋅(−8)

4. Simplify each term by performing the multiplication.

x3−6*x2+12*x−8

Final Answer

(x−2)3=x3−6*x2+12*x−8

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