Question
Factor the expression completely 12ab^3 + 20b
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To factor the expression \( 12ab^3 + 20b \) completely, we start by identifying the greatest common factor (GCF) of the two terms.
1. **Identify the coefficients:** The coefficients are 12 and 20. The GCF of 12 and 20 is 4.
2. **Identify the variable factors:** The terms have \( b \) in common. The smallest power of \( b \) present in both terms is \( b^1 \).
Combining these, the GCF of \( 12ab^3 \) and \( 20b \) is \( 4b \).
Now, we can factor out \( 4b \) from the expression:
\[
12ab^3 + 20b = 4b(3ab^2 + 5)
\]
Next, we check if \( 3ab^2 + 5 \) can be factored further. Since \( 3ab^2 + 5 \) does not have a common factor and cannot be factored using any simple methods (it is a sum of terms with no common variables), it is already in its simplest form.
Thus, the completely factored form of the expression \( 12ab^3 + 20b \) is:
\[
\boxed{4b(3ab^2 + 5)}
\]
1. **Identify the coefficients:** The coefficients are 12 and 20. The GCF of 12 and 20 is 4.
2. **Identify the variable factors:** The terms have \( b \) in common. The smallest power of \( b \) present in both terms is \( b^1 \).
Combining these, the GCF of \( 12ab^3 \) and \( 20b \) is \( 4b \).
Now, we can factor out \( 4b \) from the expression:
\[
12ab^3 + 20b = 4b(3ab^2 + 5)
\]
Next, we check if \( 3ab^2 + 5 \) can be factored further. Since \( 3ab^2 + 5 \) does not have a common factor and cannot be factored using any simple methods (it is a sum of terms with no common variables), it is already in its simplest form.
Thus, the completely factored form of the expression \( 12ab^3 + 20b \) is:
\[
\boxed{4b(3ab^2 + 5)}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.