Certainly! Let’s analyze and compare each option to find which expression is equivalent to [tex]\(3 \times (6 + 9)\)[/tex].
First, let's compute the value of the given expression:
[tex]\[3 \times (6 + 9).\][/tex]
Step 1: Compute the value inside the parentheses:
[tex]\[6 + 9 = 15.\][/tex]
Step 2: Multiply the result by 3:
[tex]\[3 \times 15 = 45.\][/tex]
Now, we'll evaluate each of the given options to see which one equals 45.
### Option A: [tex]\((3 + 6) + (3 + 9)\)[/tex]
Step 1: Compute the values inside the parentheses:
[tex]\[3 + 6 = 9\][/tex]
[tex]\[3 + 9 = 12\][/tex]
Step 2: Add the two results:
[tex]\[9 + 12 = 21\][/tex]
So, option A evaluates to 21, which is not equal to 45.
### Option B: [tex]\((3 \times 6) + (3 + 9)\)[/tex]
Step 1: Compute the values inside the parentheses:
[tex]\[3 \times 6 = 18\][/tex]
[tex]\[3 + 9 = 12\][/tex]
Step 2: Add the two results:
[tex]\[18 + 12 = 30\][/tex]
So, option B evaluates to 30, which is not equal to 45.
### Option C: [tex]\((3 + 6) + (3 \times 9)\)[/tex]
Step 1: Compute the values inside the parentheses:
[tex]\[3 + 6 = 9\][/tex]
[tex]\[3 \times 9 = 27\][/tex]
Step 2: Add the two results:
[tex]\[9 + 27 = 36\][/tex]
So, option C evaluates to 36, which is not equal to 45.
### Option D: [tex]\((3 \times 6) + (3 \times 9)\)[/tex]
Step 1: Compute the values inside the parentheses:
[tex]\[3 \times 6 = 18\][/tex]
[tex]\[3 \times 9 = 27\][/tex]
Step 2: Add the two results:
[tex]\[18 + 27 = 45\][/tex]
So, option D evaluates to 45, which is equal to 45.
Hence, the expression that is equivalent to [tex]\(3 \times (6 + 9)\)[/tex] is:
D. [tex]\((3 \times 6) + (3 \times 9)\)[/tex]
