Final answer:
The expression 15a³b - 3ab⁴ is rewritten by factoring out the greatest common factor, which is 3ab, resulting in the expression 3ab(5a² - b³). None of the given options are correct because they incorrectly use ab⁴ as the common factor instead of just 3ab.
Step-by-step explanation:
The expression 15a³b - 3ab⁴ can be rewritten by factoring out the common factor. The greatest common factor of both terms is 3ab, so we should divide each term by this common factor to simplify the expression.
By factoring out 3ab, the expression becomes:
3ab(5a² - b³)
When we distribute the 3ab back into the expression, we would get the original expression:
3ab(5a²) gives us 15a³b
and 3ab(-b³) gives us - 3ab⁴.
Therefore, the rewritten expression using a common factor is 3ab(5a² - b³), which corresponds to none of the options provided. All options incorrectly have ab⁴ as the common factor, but the highest power of b that is common in both terms is b, not b⁴.