Question

Factor
\[18p-36\] to identify the equivalent expressions.
Choose 2 answers:
Choose 2 answers:
(Choice A)
\[3(9p-12)\]
A
\[3(9p-12)\]
(Choice B)
\[9(2p-4p)\]
B
\[9(2p-4p)\]
(Choice C)
\[2(9p-18)\]
C
\[2(9p-18)\]
(Choice D)
\[18(p-2)\]
D
\[18(p-2)\]

Answer 1

To factor the expression \(18p - 36\), we can begin by identifying the greatest common factor (GCF) of the terms.

The two terms are \(18p\) and \(-36\). The GCF of \(18\) and \(36\) is \(18\).

We can factor out \(18\) from the expression:

\[
18p - 36 = 18(p - 2)
\]

Now, let's check each of the choices to identify which are equivalent to \(18p - 36\):

**Choice A**:
\[3(9p - 12)\]
Distributing \(3\):
\[
3 \cdot 9p - 3 \cdot 12 = 27p - 36 \quad (\text{not equivalent})
\]

**Choice B**:
\[9(2p - 4p)\]
This expression appears to have a mistake (it's not clear what it means, as \(2p - 4p = -2p\)):
\[
9(-2p) = -18p \quad (\text{not equivalent})
\]

**Choice C**:
\[2(9p - 18)\]
Distributing \(2\):
\[
2 \cdot 9p - 2 \cdot 18 = 18p - 36 \quad (\text{equivalent})
\]

**Choice D**:
\[18(p - 2)\]
This is exactly what we factored:
\[
18(p - 2) = 18p - 36 \quad (\text{equivalent})
\]

Based on this analysis, the two choices that are equivalent to \(18p - 36\) are:

- **Choice C**: \[2(9p - 18)\]
- **Choice D**: \[18(p - 2)\]

So the correct answers are **C** and **D**.