Apply factoring to simplify the computation: Evaluate 356 × 936 − 356 × 836 by extracting the common factor.

Introduction / Context:
Expressions of the form a*b − a*c are tailor-made for the distributive property. Recognizing and factoring out the common term avoids heavy multiplication and reduces the chance of arithmetic mistakes.

Given Data / Assumptions:

• Expression: 356 × 936 − 356 × 836.
• Common factor: 356.
• We want an exact numeric result.

Concept / Approach:
Use the distributive law: a*b − a*c = a*(b − c). This converts two large products and a subtraction into a single subtraction and one manageable multiplication, providing a neat and quick result.

Step-by-Step Solution:
Factor 356: 356 × (936 − 836).Compute the inner difference: 936 − 836 = 100.Multiply: 356 × 100 = 35600.Therefore, the value is 35600.

Verification / Alternative check:
If you compute 356 × 936 and 356 × 836 separately and then subtract, you will also reach 35600, confirming the factorization approach.

Why Other Options Are Wrong:
93600 and 34500 come from misreading the difference or misapplying the common factor.49630 resembles a random product and does not honor the factorization identity.

Common Pitfalls:
Forgetting to subtract the inner numbers first; multiplying 356 by 936 and 836 fully (time-consuming) and making a slip; swapping the terms and getting a sign error.

Final Answer:
35600