Number System — Evaluate the arithmetic expression exactly: 160 × 106 + 94 × 94. Choose the correct total from the options.

Introduction / Context:
This problem requires accurate computation with mixed products and a square term. Precision with place-value multiplication and addition is the key. Recognizing that 94 × 94 is a square can help you compute it cleanly before combining with the other product.

Given Data / Assumptions:

• We must compute 160 × 106 + 94 × 94 exactly.
• Standard integer arithmetic applies.
• No approximations are needed; the goal is the exact sum.

Concept / Approach:
Break each term into manageable parts. For the product 160 × 106, use distributive multiplication. For 94 × 94, compute the square directly (or use a near-100 adjustment if preferred), then add the two results. Double-check intermediate totals to avoid digit slips.

Step-by-Step Solution:
1) Compute 160 × 106 = 160 × (100 + 6) = 16000 + 960 = 16960.2) Compute 94 × 94. One way: 90 × 94 = 8460; add 4 × 94 = 376; total = 8460 + 376 = 8836.3) Add results: 16960 + 8836 = 25796.4) Therefore, the exact value is 25796.

Verification / Alternative check:
Alternative square check: (100 − 6)^2 = 10000 − 2*100*6 + 6^2 = 10000 − 1200 + 36 = 8836. Adding to 16960 again gives 25796, confirming consistency.

Why Other Options Are Wrong:
25876 and 25716 are common digit-transposition errors after addition; 24796 undercounts by 1000 (missed carry); 20032 ignores most of the second term or miscomputes both products.

Common Pitfalls:
Dropping a zero in 160 × 106; mixing up 94 × 94 with 94 × 90; forgetting to carry during addition; confusing (a − b)^2 with a^2 − b^2.

Final Answer:
25796