Rewrite the following numerical expression in an equivalent form using the distributive property: 36 + 54. Select all that apply.(1 point)

Question

Responses

3(12 + 18)
3(12 + 18)

3(12 + 54)
3(12 + 54)

6(6 + 9)
6(6 + 9)

6(6 + 54)
6(6 + 54)

9(4 + 6)
9(4 + 6)

9(4 + 54)

Answer 1

To rewrite the expression \(36 + 54\) using the distributive property, we can factor out a common factor.

1. First, let's compute \(36 + 54 = 90\).

2. Now, we can look for a factorization that equals \(90\):

   • Factoring out \(3\):
     • \(36 + 54 = 3 \times 12 + 3 \times 18 = 3(12 + 18)\)
   • Factoring out \(6\):
     • \(36 + 54 = 6 \times 6 + 6 \times 9 = 6(6 + 9)\)
   • Factoring out \(9\):
     • \(36 + 54 = 9 \times 4 + 9 \times 6 = 9(4 + 6)\)

The other options, \(3(12 + 54)\) and \(6(6 + 54)\), do not correctly factor 90, as they do not represent equivalent forms of \(90\).

Therefore, the equivalent forms using the distributive property are:

1. 3(12 + 18)
2. 6(6 + 9)
3. 9(4 + 6)

These are the correct answers.