What is the factorisation of (25p^2-36q^2)?
Answer and explanation
Correct answer: \((5p+6q)(5p-6q)\)
\(25p^2-36q^2=(5p)^2-(6q)^2\), which is a difference of two squares. Using \(a^2-b^2=(a+b)(a-b)\), we get \((5p+6q)(5p-6q)\). Options A and D are squares of a difference and a sum respectively; their expansions contain a \(pq\) term, which is absent in the given expression. Exam tip: identify the square roots first, then use \((a+b)(a-b)\) for a difference of squares.
Frequently asked questions
What is the correct answer to this question?
\((5p+6q)(5p-6q)\)
Why is this the correct answer?
\(25p^2-36q^2=(5p)^2-(6q)^2\), which is a difference of two squares. Using \(a^2-b^2=(a+b)(a-b)\), we get \((5p+6q)(5p-6q)\). Options A and D are squares of a difference and a sum respectively; their expansions contain a \(pq\) term, which is absent in the given expression. Exam tip: identify the square roots first, then use \((a+b)(a-b)\) for a difference of squares.
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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