Let's simplify the given expression:

\[
32 \cdot bx \cdot 2 + 16 \cdot bxy + 2 \cdot by \cdot 2
\]

### Step 1: Simplify each term
1. \( 32 \cdot bx \cdot 2 = 64bx \)
2. \( 16 \cdot bxy = 16bxy \)
3. \( 2 \cdot by \cdot 2 = 4by \)

### Step 2: Combine all terms
The simplified expression is:
\[
64bx + 16bxy + 4by
\]

Would you like more details or have any questions? Here are 5 related problems you can try:

1. Simplify \( 5a \cdot 3b + 10ab \).
2. Factor the expression \( 64bx + 16bxy + 4by \).
3. Expand and simplify \( 4(bx + by) \).
4. Simplify \( 3x^2 \cdot 4x + 2x^3 \).
5. Combine like terms: \( 7ab + 3a - 4ab + 2a \).

**Tip:** Look for common factors or terms that can be factored out to simplify complex expressions.

Learn how to simplify the expression 32bx2 + 16bxy + 2by2 step-by-step with detailed explanations. This problem involves algebraic concepts such as polynomials and simplification techniques. Suitable for high school students.

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