Question

factor
n³-125
hint: difference of two cubes

○ (n-5)³

○ (n+5)(n²-5n+25)

○ (n-5)(n²+5n+25)

○ (n-5)(n²+25)

Explanation:

Step1: Recall the difference of cubes formula

The formula for the difference of two cubes is $a^3 - b^3=(a - b)(a^2+ab + b^2)$.

Step2: Identify \(a\) and \(b\) in the given expression

For the expression \(n^3-125\), we can rewrite \(125\) as \(5^3\). So, \(a = n\) and \(b = 5\) since \(n^3-125=n^3 - 5^3\).

Step3: Apply the difference of cubes formula

Substitute \(a=n\) and \(b = 5\) into the formula \(a^3 - b^3=(a - b)(a^2+ab + b^2)\). We get:
\(n^3-5^3=(n - 5)(n^2+(n\times5)+5^2)=(n - 5)(n^2 + 5n+25)\)

Answer:

\((n - 5)(n^2 + 5n+25)\) (corresponding to the option \((n - 5)(n^2+5n + 25)\))