Simplify (x-2)^3

Problem

(x−2)3

Solution

1. Identify the expression as a binomial cube of the form (a−b)3

2. Apply the formula for the cube of a binomial, which is (a−b)3=a3−3*a2*b+3*a*b2−b3

3. Substitute a=x and b=2 into the formula.

4. Expand the terms:

x3−3*(x2)*(2)+3*(x)*(2)−2

5. Simplify each term by performing the multiplication and exponentiation:

x3−6*x2+3*(x)*(4)−8

6. Combine the remaining constants:

x3−6*x2+12*x−8

Final Answer

(x−2)3=x3−6*x2+12*x−8

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