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\[ \text{احسب } 2011^2 - 2010^2 \text{؟} \]

Ask by Weaver Greene. in Morocco
Mar 13,2025

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\( 2011^2 - 2010^2 = 4021 \)

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يمكن استخدام صيغة الفرق بين مربعين، والتي تنص على أن \( a^2 - b^2 = (a - b)(a + b) \). في هذه الحالة، لدينا: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] إذًا، الناتج هو \( 4021 \). في الرياضيات، تُظهر المشكلات من هذا النوع بوضوح كيف يمكن تبسيط المسائل المعقدة باستخدام نظريات أساسية. تخيل كم سيكون الأمر معقداً لو حسبنا كل مربع بشكل منفصل! تكمن العبقرية في تبسيط الأمور.

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