12 () 34 = 56
38 () 75 = 136
2021 () 9002 = ....

Let's analyze the given equations to identify the pattern:

1. \(12 \, () \, 34 = 56\)
2. \(38 \, () \, 75 = 136\)
3. \(2021 \, () \, 9002 = ?\)

We need to determine the operation that connects the numbers on the left-hand side to the result on the right-hand side.

### First equation: 
\(12 \, () \, 34 = 56\)
One possible approach is to check if adding the numbers works:
\[
12 + 34 = 46
\]
However, this gives 46, not 56.

Instead, let's check if multiplying the numbers' digits might work:
\[
(1 \times 2) + (3 \times 4) = 2 + 12 = 14
\]
This doesn't match either.

Another idea is to subtract the smaller number from the larger number:
\[
34 - 12 = 22
\]
But this doesn't fit 56 either. So we can try squaring:

\[
\sqrt{34}^2 + \.
Let's

Explore the pattern recognition puzzle: 12 () 34 = 56, 38 () 75 = 136, and solve for 2021 () 9002. Understand different mathematical approaches, including arithmetic operations and number pattern analysis. Suitable for students in Grades 6-8.

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