Which of the following correctly represents the factorised form of a^2-b^2 ?
Answer and explanation
Correct answer: \((a-b)(a+b)\)
The difference-of-squares identity is \(a^2-b^2=(a-b)(a+b)\). On multiplying, the middle terms \(-ab\) and \(+ab\) cancel. In contrast, \((a-b)^2\) contains a \(-2ab\) term. Exam tip: for two squared terms with subtraction, look for the sum-and-difference factors.
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 \(a^2-b^2=(a-b)(a+b)\). On multiplying, the middle terms \(-ab\) and \(+ab\) cancel. In contrast, \((a-b)^2\) contains a \(-2ab\) term. Exam tip: for two squared terms with subtraction, look for the sum-and-difference factors.
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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