Compute the exact product: 786 multiplied by 964. Present the full integer result (no rounding).

Introduction / Context:
This problem tests accuracy and speed in multiplying two three-digit integers. While it can be done with a calculator, the purpose in aptitude settings is to practice reliable breakdown methods such as distributive expansion.

Given Data / Assumptions:

• Numbers: 786 and 964.
• Operation: multiplication.
• Desired output: exact integer product.

Concept / Approach:
Use distributive multiplication to reduce errors: 964 = 1000 − 36. Then 786 × 964 = 786 × (1000 − 36) = 786000 − 786 × 36. Alternatively, split 964 as (900 + 60 + 4) and add partial products.

Step-by-Step Solution:

Verification / Alternative check:
Check with partial sums: 786*(900) = 707400; 786*(60) = 47160; 786*(4) = 3144. Sum 707400 + 47160 + 3144 = 757704, matching the result.

Why Other Options Are Wrong:
759276, 749844, 756984, and 75416 are typical of digit-slip or partial-product mistakes. Only 757704 is consistent across multiple decomposition methods.

Common Pitfalls:
Misplacing zeros when multiplying by powers of 10, or mixing up subtraction in the 1000 − 36 decomposition. Always recompute small components (like 786 × 36) carefully.

Final Answer:
757704