Which expression shows 18 + 15 written as a product of two factors

Which expression shows 18 + 15 written as a product of two factors?
A. 3(6+5)

B. 6(3+5)

C. 3(9+5)

D. 6(3+2)

The Correct Answer and Explanation is:

To express the sum (18 + 15) as a product of two factors, we first simplify the expression. The sum can be rewritten as follows:

[
18 + 15 = 33
]

Next, we need to find two factors that multiply to give 33. The options provided are:

A. (3(6 + 5))
B. (6(3 + 5))
C. (3(9 + 5))
D. (6(3 + 2))

We will evaluate each option to see which one equates to (33):

1. Option A: (3(6 + 5))
   Calculating inside the parentheses:
   (6 + 5 = 11)
   Now multiply:
   (3 \times 11 = 33)
   This option is correct.
2. Option B: (6(3 + 5))
   Calculating inside the parentheses:
   (3 + 5 = 8)
   Now multiply:
   (6 \times 8 = 48)
   This option is incorrect.
3. Option C: (3(9 + 5))
   Calculating inside the parentheses:
   (9 + 5 = 14)
   Now multiply:
   (3 \times 14 = 42)
   This option is incorrect.
4. Option D: (6(3 + 2))
   Calculating inside the parentheses:
   (3 + 2 = 5)
   Now multiply:
   (6 \times 5 = 30)
   This option is incorrect.

After evaluating all the options, we find that Option A is the only expression that correctly shows (18 + 15) as a product of two factors.

In conclusion, (18 + 15) can be expressed as (3(6 + 5)), which simplifies to (3 \times 11), resulting in (33). This is a useful skill in algebra, as expressing sums as products can simplify calculations and help in factoring or solving equations. Recognizing how to manipulate numbers and expressions is fundamental in understanding more complex mathematical concepts. Therefore, the correct answer is A: (3(6 + 5)).