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=a^3−3*a^2*b+3*a*b^2−b^3

3. Substitute a=x and b=5 into the formula.

4. Expand the terms: x^3−3*(x^2)*(5)+3*(x)*(5^2)−5^3

5. Simplify the coefficients and powers: x^3−15*x^2+3*(x)*(25)−125

6. Calculate the final values: x^3−15*x^2+75*x−125

Final Answer

(x−5)^3=x^3−15*x^2+75*x−125

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