Asked by hola
Identify the correct factorization:
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)
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)
Answers
Answered by
GPT-4o mini
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)**
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)**