Question

question
factor $125 - x^3$ completely.
answer attempt 1 out of 2
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Explanation:

Step1: Identify the formula for difference of cubes

The expression \(125 - x^3\) can be written as \(5^3 - x^3\). The formula for the difference of cubes is \(a^3 - b^3=(a - b)(a^2+ab + b^2)\). Here, \(a = 5\) and \(b=x\).

Step2: Apply the difference of cubes formula

Substitute \(a = 5\) and \(b = x\) into the formula:
\(5^3 - x^3=(5 - x)(5^2+5\times x+x^2)\)
Simplify \(5^2\) to get \(25\), so the expression becomes \((5 - x)(25 + 5x+x^2)\) or \((5 - x)(x^2 + 5x+25)\) (the order of terms in the quadratic factor does not matter for factoring).

Answer:

\((5 - x)(x^2 + 5x + 25)\)