Use a^2 − b^2 factorization with decimals: Evaluate 13.065^2 − 3.065^2 by rewriting it as (a − b)(a + b) and computing quickly.

Introduction / Context:The classic identity a^2 − b^2 = (a − b)(a + b) is a powerful shortcut, especially with decimals. It replaces squaring and subtracting with two additions/subtractions and one multiplication, greatly reducing error likelihood and saving time.

Given Data / Assumptions:

• a = 13.065, b = 3.065.
• Compute a^2 − b^2.

Concept / Approach:Apply a^2 − b^2 = (a − b)(a + b). The numbers are chosen so that a − b is an integer, making the product particularly simple to evaluate accurately.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 159.5 and 141.6: Result from mis-adding a + b or misplacing decimals.
• 100: Confuses a^2 − b^2 with (a − b)^2 or only takes a − b.

Common Pitfalls:

• Losing decimal places during addition.
• Attempting the full squaring, increasing arithmetic risk.

Final Answer: