Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Evaluate efficiently using expression structure
Problem
Evaluate \(101^{2}-99^{2}\) efficiently using structure.
Big Picture
What this problem is really about
The expression’s difference-of-squares structure replaces two large square calculations with a small difference and sum. We’ll apply the conjugate identity to the two square bases, evaluate those simple factors, multiply them, and use direct squaring only as an independent check.
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