Simplify (x-5)^3

Problem

(x−5)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=5 into the formula.

4. Expand the terms: x3−3*(x2)*(5)+3*(x)*(5)−5

5. Simplify the coefficients and powers: x3−15*x2+3*(x)*(25)−125

6. Calculate the final values: x3−15*x2+75*x−125

Final Answer

(x−5)3=x3−15*x2+75*x−125

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