Arithmetic Simplification — Common Factor Method Evaluate: 9856 × 156 + 9856 × 844. Use factoring to simplify the computation.

Introduction / Context:This expression is designed to reward recognition of the distributive property. Rather than multiply two large products separately, factor out the common term to turn the problem into a single, easy multiplication.

Given Data / Assumptions:

• Expression: 9856 × 156 + 9856 × 844.
• All numbers are integers.
• Standard arithmetic rules apply.

Concept / Approach:Use the distributive property: a*b + a*c = a*(b + c). Here a = 9856, b = 156, c = 844. Adding the small numbers first is simpler and reduces computational effort dramatically.

Step-by-Step Solution:1) Factor: 9856 × 156 + 9856 × 844 = 9856 × (156 + 844).2) Add inside the parentheses: 156 + 844 = 1000.3) Multiply: 9856 × 1000 = 9,856,000.4) Therefore, the value is 9,856,000.

Verification / Alternative check:If you computed each product separately and added, you would reach the same total, but with more work. The factorization method is quicker and less error-prone.

Why Other Options Are Wrong:Other totals result from arithmetic slips, mis-adding 156 + 844, or misplacing zeros when multiplying by 1000.

Common Pitfalls:Ignoring the common factor; performing two large multiplications and making place-value mistakes; forgetting to append three zeros when multiplying by 1000.

Final Answer:9856000