Let's evaluate each statement step by step:
Statement #1:
\[ 3 \cdot 20 = 4(6 + 9) \]
Calculating both sides:
- Left side: \[ 3 \cdot 20 = 60 \]
- Right side: \[ 4(6 + 9) = 4 \cdot 15 = 60 \]
So, Statement #1 is true.
Statement #2:
\[ 4 \cdot 12 = 6 \cdot (8 \cdot 2) + 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8 \]
Calculating both sides:
- The first part, \( 4 \cdot 12 = 48 \).
Now let's calculate the right side:
- \( 6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96 \)
- \( 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \)
So, \[ 6 \cdot (8 \cdot 2) + 12 + 6 \cdot \sqrt{64} = 96 + 60 = 156 \]
Now let's calculate \( 2 \cdot 4 \cdot 8 \): \[ 2 \cdot 4 \cdot 8 = 64 \]
Since \( 48 \neq 156 \) and \( 48 \neq 64 \), Statement #2 is false.
Statement #3:
\[ 4 \cdot 18 - 4 \cdot 6 = 4^2 + 4 \cdot 8 \]
Calculating both sides:
-
Left side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]
-
Right side: \[ 4^2 + 4 \cdot 8 = 16 + 32 = 48 \]
So, Statement #3 is true.
Conclusion:
The statements that are true are 1 and 3.
Thus, the answer is 1 and 3.