What is the correct factorisation of (81a^2-49b^2)?
Answer and explanation
Correct answer: \((9a+7b)(9a-7b)\)
\(81a^2-49b^2=(9a)^2-(7b)^2\). Applying the identity \(x^2-y^2=(x+y)(x-y)\) gives \((9a+7b)(9a-7b)\). Options B and D are perfect squares and would produce a middle term of \(\mp126ab\), which is absent in the given expression. Exam tip: identify the square roots of both terms, then write one sum factor and one difference factor.
Frequently asked questions
What is the correct answer to this question?
\((9a+7b)(9a-7b)\)
Why is this the correct answer?
\(81a^2-49b^2=(9a)^2-(7b)^2\). Applying the identity \(x^2-y^2=(x+y)(x-y)\) gives \((9a+7b)(9a-7b)\). Options B and D are perfect squares and would produce a middle term of \(\mp126ab\), which is absent in the given expression. Exam tip: identify the square roots of both terms, then write one sum factor and one difference factor.
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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