To simplify the expression \( 3a \times 4b \times 2a \times 5c \times 3b \times c \), we can follow these steps:

1. **Group the constants**: 
   Multiply the numerical constants together:
   \[
   3 \times 4 \times 2 \times 5 \times 3 = 360
   \]

2. **Group the variables**:
   - For \(a\): \( a \times a = a^2 \)
   - For \(b\): \( b \times b = b^2 \)
   - For \(c\): \( c \times c = c^2 \)

Now, combine everything together:

\[
360 \times a^2 \times b^2 \times c^2 = 360a^2b^2c^2
\]

The simplified expression is:
\[
360a^2b^2c^2
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify algebraic expressions involving variables and constants?
2. What are the rules for multiplying variables with exponents?
3. How can you factor expressions like the one above?
4. How do you handle division in similar algebraic expressions?
5. How can you apply these principles to real-world problems?

**Tip**: When multiplying variables, remember to add their exponents if the bases are the same.

Learn how to simplify the algebraic expression 3a × 4b × 2a × 5c × 3b × c step-by-step. This problem involves the multiplication of constants and variables, and applies the laws of exponents. Suitable for students in Grades 6-8.

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