Identify the correct factorization:

Question

36y^2−24y

Responses

12y(3y - 2)
12y(3y - 2)

2y(18y - 12y)
2y(18y - 12y)

3y(12y - 8y)
3y(12y - 8y)

4(9y - 6)

Answer 1

To factor the expression \(36y^2 - 24y\), we can start by finding the greatest common factor (GCF) of the two terms.

1. The GCF of \(36y^2\) and \(24y\) is \(12y\).
2. Factor out \(12y\):

\[ 36y^2 - 24y = 12y(3y - 2) \]

Now, let's verify each of the responses:

1. 12y(3y - 2) - This is correct.
2. 2y(18y - 12y) - This simplifies to \(2y(6y)\), which is not equivalent to the original expression.
3. 3y(12y - 8y) - This simplifies to \(3y(4y)\), which is also not equivalent.
4. 4(9y - 6) - This does not simplify to the original expression.

Thus, the correct factorization is:

12y(3y - 2)