volume_mute
Match Algebraic Identities
publish date: 2026/05/23 05:43:43.660245 UTC
volume_muteMatch each algebraic expression on the left with its equivalent identity on the right.
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Expression
\(a^3 + b^3\)
\(a^3 - b^3\)
\((a+b)^2 - (a-b)^2\)
\(a^2 - b^2\)
Identity
\((a+b)(a-b)\)
\(4ab\)
\((a+b)(a^2 - ab + b^2)\)
\((a-b)(a^2 + ab + b^2)\)
Correct Answer
(1) \(a^3 + b^3\),\((a+b)(a^2 - ab + b^2)\)
(2) \(a^3 - b^3\),\((a-b)(a^2 + ab + b^2)\)
(3) \((a+b)^2 - (a-b)^2\),\(4ab\)
(4) \(a^2 - b^2\),\((a+b)(a-b)\)
Explanation
These are fundamental algebraic identities: difference of squares, sum/difference of cubes, and the difference of squares of sums. They are used extensively in simplifying expressions and solving equations.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012