factor this expression

Question

24y^4-6y^2

Answer 1

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: \[ 6y^2(2y - 1)(2y + 1) \]