Find Equivalent Expressions for 16-4c: Algebraic Comparison

To solve this problem, we'll follow these steps:

• Step 1: Identify the greatest common factor (GCF) of the terms in the expression $16 - 4c$.
• Step 2: Factor out the GCF from both terms.
• Step 3: Compare the factored expression with the provided choices to find the equivalent expression.

Let's work through each step:

Step 1: Identify the GCF.
The terms in the expression are $16$ and $-4c$. The greatest common factor of $16$ and $4$ (coefficient of $c$) is $4$.

Step 2: Factor out the GCF.
Factor $4$ out from each term in the expression:
$16 - 4c = 4 \times 4 - 4 \times c = 4(4 - c)$.

Step 3: Compare with the choices.
We factorized $16 - 4c$ to get $4(4 - c)$. Now we compare it with the provided choices:

• Choice 1: $4(12 - c)$ does not match our expression.
• Choice 2: $4(4 - 4c)$ is also not equivalent.
• Choice 3: $4(2 - c)$ is not equivalent.
• Choice 4: $4(4 - c)$ matches our expression precisely.

Therefore, the expression equivalent to $16 - 4c$ is $\boxed{4(4 - c)}$.