Let's evaluate the given expression and compare it with each of the given options to find which ones are equivalent.
The original expression we are given is:
[tex]\[ 7 \cdot (6 + 3) \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ 6 + 3 = 9 \][/tex]
Now multiply by 7:
[tex]\[ 7 \cdot 9 = 63 \][/tex]
So the original expression evaluates to 63.
Now, let's analyze each option to see which ones match this result:
Option A: [tex]\( 7 \cdot 9 \)[/tex]
[tex]\[ 7 \cdot 9 = 63 \][/tex]
This is equivalent to the original expression.
Option B: [tex]\( 7 \cdot 3 + 7 \cdot 6 \)[/tex]
Let's apply the distributive property:
[tex]\[ 7 \cdot 3 + 7 \cdot 6 = 21 + 42 = 63 \][/tex]
This is also equivalent to the original expression.
Option C: [tex]\( 7 \cdot 18 \)[/tex]
[tex]\[ 7 \cdot 18 = 126 \][/tex]
This is not equivalent to the original expression.
Option D: [tex]\( 7 \cdot 6 + 7 \cdot 3 \)[/tex]
Again, let's apply the distributive property:
[tex]\[ 7 \cdot 6 + 7 \cdot 3 = 42 + 21 = 63 \][/tex]
This is equivalent to the original expression.
Therefore, the options that are equivalent to the given expression [tex]\( 7 \cdot (6 + 3) \)[/tex] are:
- Option A [tex]\( 7 \cdot 9 \)[/tex]
- Option B [tex]\( 7\cdot 3 + 7 \cdot 6 \)[/tex]
- Option D [tex]\( 7 \cdot 6 + 7 \cdot 3 \)[/tex]
So, the correct answers are A, B, and D.
