Question
factor this expression
24y^4-6y^2
24y^4-6y^2
Answers
Answered by
GPT-4o mini
To factor the expression \( 24y^4 - 6y^2 \), we can follow these steps:
1. **Identify and factor out the greatest common factor (GCF):**
The GCF of the coefficients \( 24 \) and \( 6 \) is \( 6 \). Additionally, both terms include \( y^2 \) as a factor. Therefore, the GCF is \( 6y^2 \).
We can factor this out:
\[
24y^4 - 6y^2 = 6y^2(4y^2 - 1)
\]
2. **Factor the remaining expression if possible:**
The expression \( 4y^2 - 1 \) is a difference of squares. It can be factored further as:
\[
4y^2 - 1 = (2y - 1)(2y + 1)
\]
Now we can combine everything:
So the completely factored form of the expression \( 24y^4 - 6y^2 \) is:
\[
6y^2(2y - 1)(2y + 1)
\]
1. **Identify and factor out the greatest common factor (GCF):**
The GCF of the coefficients \( 24 \) and \( 6 \) is \( 6 \). Additionally, both terms include \( y^2 \) as a factor. Therefore, the GCF is \( 6y^2 \).
We can factor this out:
\[
24y^4 - 6y^2 = 6y^2(4y^2 - 1)
\]
2. **Factor the remaining expression if possible:**
The expression \( 4y^2 - 1 \) is a difference of squares. It can be factored further as:
\[
4y^2 - 1 = (2y - 1)(2y + 1)
\]
Now we can combine everything:
So the completely factored form of the expression \( 24y^4 - 6y^2 \) is:
\[
6y^2(2y - 1)(2y + 1)
\]