Question

Factor
\[16a+72\] to identify the equivalent expressions.
Choose 2 answers:
Choose 2 answers:
(Choice A)
\[4(4a+18)\]
A
\[4(4a+18)\]
(Choice B)
\[8(2a+9)\]
B
\[8(2a+9)\]
(Choice C)
\[2(8+36a)\]
C
\[2(8+36a)\]
(Choice D)
\[2(8a+72)\]
D
\[2(8a+72)\]

Answer 1

To factor the expression \(16a + 72\), we first identify the greatest common factor (GCF) of the two terms.

The coefficients are 16 and 72. The GCF of 16 and 72 is 8. Therefore, we can factor out 8 from the expression:

\[
16a + 72 = 8(2a + 9)
\]

Now let's check the options provided:

1. **Choice A: \(4(4a + 18)\)**
- If we distribute \(4\), we get \(16a + 72\). So, this expression is equivalent, but it’s not the most factored form since the GCF is 8, not 4.

2. **Choice B: \(8(2a + 9)\)**
- This matches our derived factored form, making it equivalent to \(16a + 72\).

3. **Choice C: \(2(8 + 36a)\)**
- If we distribute \(2\), we get \(16a + 72\) which is also equivalent, but again, this isn't the most factored form since we can factor it more efficiently.

4. **Choice D: \(2(8a + 72)\)**
- If we distribute \(2\), we get \(16a + 144\), which is not equivalent to \(16a + 72\).

The two correct answers, therefore, are:

- **Choice A**: \(4(4a + 18)\)
- **Choice B**: \(8(2a + 9)\)

So the final selection is **A and B**.