Determine which of the following statements is/are true:

#1: 3⋅20=4(6+9)
#2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8
#3: 4⋅18−4⋅6=4^2+4⋅8
(1 point)

2 and 3
1 and 2
1
1 and 3

1 answer

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.