Final answer:
The expression 216x³ + 9y¹µ is factored by first identifying the greatest common factor, which is 9. After factoring out 9, the final expression is 9(24x³ + y¹µ). No further factoring is possible as the expression inside the parentheses does not have common factors.
Step-by-step explanation:
Factoring the Expression
To factor the expression 216x³ + 9y¹µ completely, it is helpful to look for a greatest common factor (GCF) first. Since both terms have a factor of 9, we can start by factoring out 9:
9(24x³ + y¹µ)
Looking at the remaining expression inside the parentheses, there are no further common algebraic factors as one term contains x and the other contains y. Therefore, after factoring out the GCF, the expression is factored as much as possible.
The final factored form is 9(24x³ + y¹µ).
Cubing of Exponentials
In case of cubing of exponentials, the process involves cubing the numerical coefficient and multiplying the exponent by 3. However, since the given expression does not lend itself to cubing, this rule is not applicable here.