To solve the expression \(353 \times 26 - 14 \times 353 + 12 \times 147\), we follow the order of operations (PEMDAS/BODMAS):

1. **Multiplication**:
   \[
   353 \times 26 = 9178
   \]
   \[
   14 \times 353 = 4942
   \]
   \[
   12 \times 147 = 1764
   \]

2. **Subtraction and Addition**:
   \[
   9178 - 4942 + 1764
   \]
   \[
   9178 - 4942 = 4236
   \]
   \[
   4236 + 1764 = 6000
   \]

So, the final answer is \(6000\).

Would you like any more details or have any questions?

Here are 5 related questions:
1. How would you factor the expression \(353 \times 26 - 14 \times 353 + 12 \times 147\)?
2. What is the general approach to solving expressions with multiple operations?
3. How do you distribute multiplication over addition and subtraction in algebraic expressions?
4. How does the order of operations affect the outcome of calculations?
5. What happens if we change the sequence of operations in the expression?

**Tip:** Always perform multiplication and division before addition and subtraction in any mathematical expression.

Learn how to calculate the result of the expression 353 times 26 minus 14 times 353 plus 12 times 147 using the order of operations (PEMDAS/BODMAS). This problem involves arithmetic operations including multiplication, subtraction, and addition. Suitable for students in Grades 5-7.

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