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What is the factor form of ( a^2-b^2 )?
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Answer and explanation
Correct answer: \((a+b)(a-b)\)
The difference-of-squares identity is \(a^2-b^2=(a+b)(a-b)\). Therefore, \((a+b)(a-b)\) is the correct factor form. In contrast, \((a-b)^2=a^2-2ab+b^2\), so it is not equal to \(a^2-b^2\). Exam tip: whenever you see \(x^2-y^2\), factor it as \((x+y)(x-y)\).
Frequently asked questions
What is the correct answer to this question?
\((a+b)(a-b)\)
Why is this the correct answer?
The difference-of-squares identity is \(a^2-b^2=(a+b)(a-b)\). Therefore, \((a+b)(a-b)\) is the correct factor form. In contrast, \((a-b)^2=a^2-2ab+b^2\), so it is not equal to \(a^2-b^2\). Exam tip: whenever you see \(x^2-y^2\), factor it as \((x+y)(x-y)\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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