Factor x^3-125

Problem

x3−125

Solution

1. Identify the expression as a difference of two cubes by rewriting the constant term as a power of 3.

x3−5

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

Let *a=x* and *b=5

3. Substitute the values of a and b into the factoring pattern.

(x−5)*(x2+(x)*(5)+5)

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

(x−5)*(x2+5*x+25)

Final Answer

x3−125=(x−5)*(x2+5*x+25)

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