Which is the correct factor form of ( 121a^2-49b^2 )?
Answer and explanation
Correct answer: \((11a+7b)(11a-7b)\)
\(121a^2-49b^2=(11a)^2-(7b)^2\). Applying the difference-of-squares identity \(x^2-y^2=(x+y)(x-y)\) gives \((11a+7b)(11a-7b)\). Options B and C are perfect squares, so their expansions contain a middle term \(\pm154ab\), which is absent in the given expression. Exam tip: first rewrite each term as a perfect square, then check for the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\((11a+7b)(11a-7b)\)
Why is this the correct answer?
\(121a^2-49b^2=(11a)^2-(7b)^2\). Applying the difference-of-squares identity \(x^2-y^2=(x+y)(x-y)\) gives \((11a+7b)(11a-7b)\). Options B and C are perfect squares, so their expansions contain a middle term \(\pm154ab\), which is absent in the given expression. Exam tip: first rewrite each term as a perfect square, then check for the difference-of-squares identity.
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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