Factor 125-x^3

Problem

125−x3

Solution

1. Identify the expression as a difference of two cubes, which follows the form a3−b3

2. Rewrite each term as a perfect cube to find the values of a and b

125=5

x3=(x)3

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

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

(5−x)*(5+5*x+x2)

5. Simplify the terms inside the second set of parentheses.

(5−x)*(25+5*x+x2)

Final Answer

125−x3=(5−x)*(25+5*x+x2)

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