Essay

Standard Operating Procedure for Binomial Squaring

You are drafting a section of a technical training manual for a precision manufacturing company. The manual needs to explain how to expand expressions like (425)2(4 - 2\sqrt{5})^2 using the Binomial Squares Pattern: (ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2.

Describe the three-step process for expanding this specific expression before any terms are simplified or combined. In your response, identify the value of the first squared term (a2a^2), the value of the middle term (2ab2ab), and the value of the final squared term (b2b^2). Specifically, explain the rule used to calculate the value of the final squared term ((25)2(2\sqrt{5})^2).

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Updated 2026-04-19

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