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Algebraic Identity: Sum of Squares

publish date: 2026/05/23 05:43:43.072105 UTC

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Which of the following is a correct algebraic identity?

\((a+b)^2 = a^2 + b^2\)

\((a+b)^2 = a^2 + 2ab + b^2\)

\((a+b)^2 = a^2 - 2ab + b^2\)

\((a+b)^2 = a^2 + b^2 - ab\)

Correct Answer

\((a+b)^2 = a^2 + 2ab + b^2\)

Explanation

The identity \((x + y)^2 = x^2 + y^2 + 2xy\) holds for all real values of \(x\) and \(y\). A common error is to write \((a+b)^2 = a^2 + b^2\), which omits the cross-product term \(2ab\).

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

Quizzes you can take where this question appears

Algebraic Notations and Symbolic Structures