Question

factor each sum or difference of cubes.
$m^3 - 27n^3$
answer

Explanation:

Step1: Recall the formula for difference of cubes

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

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

In the expression \(m^3-27n^3\), we can rewrite \(27n^3\) as \((3n)^3\). So, \(a = m\) and \(b = 3n\).

Step3: Apply the difference of cubes formula

Substitute \(a = m\) and \(b = 3n\) into the formula \(a^3 - b^3=(a - b)(a^2+ab + b^2)\).
We get \((m-(3n))(m^2+m\times(3n)+(3n)^2)\).
Simplify the terms: \((m - 3n)(m^2+3mn + 9n^2)\).

Answer:

\((m - 3n)(m^2+3mn + 9n^2)\)