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Answer
The expression \(12y - 16\) factored is \(4(3y - 4)\).
Solution
It looks like you're working on simplifying or factoring the expression \(12y - 16\). Let's go through the steps to factor this expression.
### Step 1: Identify the Greatest Common Factor (GCF)
First, determine the GCF of the coefficients (numbers) in the expression.
- The coefficients are **12** (from \(12y\)) and **16** (from \(-16\)).
- The GCF of 12 and 16 is **4**.
### Step 2: Factor Out the GCF
Now, factor out the GCF from each term in the expression.
\[
12y - 16 = 4 \times 3y - 4 \times 4
\]
\[
12y - 16 = 4(3y) - 4(4)
\]
\[
12y - 16 = 4(3y - 4)
\]
### Final Factored Form
\[
12y - 16 = \boxed{4(3y - 4)}
\]
So, the expression \(12y - 16\) factored by its greatest common factor is \(4(3y - 4)\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
This expression, \( 12y - 16 \), can be simplified or factored. If you factor out the greatest common factor, which is 4, you get \( 4(3y - 4) \). Factoring can be a handy skill! It helps make complex equations easier to work with, especially when solving for values of \( y \). In real-world scenarios, expressions like this can represent various situations, such as calculating profit where \( y \) could represent the number of items sold and the coefficients reflect cost and expenses. Understanding how to manipulate these expressions can enhance your problem-solving abilities in everyday contexts!
