We will evaluate each statement one by one to determine their truthfulness.
Statement #1: \( 3 \cdot 20 = 4(6 + 9) \)
Calculating the left side: \[ 3 \cdot 20 = 60 \]
Now calculating the right side: \[ 4(6 + 9) = 4 \cdot 15 = 60 \]
Since both sides are equal, Statement #1 is true.
Statement #2: \( 4 \times 12 = 6 \times (8 \times 2) + 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8 \)
We will break this down step by step:
Calculating \( 4 \times 12 \): \[ 4 \times 12 = 48 \]
Now, let’s evaluate the right-hand side: Calculating \( 6 \times (8 \times 2) \): \[ 8 \times 2 = 16 \] \[ 6 \times 16 = 96 \]
Now calculating \( 6 \cdot \sqrt{64} \): \[ \sqrt{64} = 8 \quad \text{thus,} \quad 6 \cdot 8 = 48 \]
Now adding \( 12 + 48 \): \[ 12 + 48 = 60 \]
Therefore, the right-hand side becomes: \[ 96 + 60 = 156 \]
Finally, calculating \( 2 \cdot 4 \cdot 8 \): \[ 2 \cdot 4 = 8 \quad \text{and} \quad 8 \cdot 8 = 64 \]
The right-hand side equals: \[ 156 = 64 \quad \text{is false.} \]
So, Statement #2 is false.
Statement #3: \( 4 \cdot 18 - 4 \cdot 6 = 4^2 + 4 \cdot 8 \)
Calculating the left side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]
Now calculating the right side: \[ 4^2 + 4 \cdot 8 = 16 + 32 = 48 \]
Since both sides are equal, Statement #3 is true.
In summary, Statements #1 and #3 are true while Statement #2 is false.
Thus, the correct option is: \[ \boxed{1 \text{ and } 3} \]
1 answer