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Problem 45

Algebra Difficulty 1.0 Prove it UKMT Senior Kangaroo · United Kingdom · 2025

What is the value of (2025+20)2+(2025+25)2(202520)2(202525)21000\dfrac{(2025 + 20)^2 + (2025 + 25)^2 - (2025 - 20)^2 - (2025 - 25)^2}{1000}, rounded up to the next integer?

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.