Which of the following expressions can be factorised as a product of two conjugate binomials?
Answer and explanation
Correct answer: \(16a^2-25b^2\)
\(16a^2-25b^2=(4a)^2-(5b)^2\) is a difference of two squares. Using \(p^2-q^2=(p+q)(p-q)\), it factorises as \((4a+5b)(4a-5b)\), a pair of conjugate binomials. Option C factorises as \((4a-5b)^2\); its two binomials are identical, not conjugates. Exam tip: look for a minus sign between two perfect-square terms when identifying conjugate factors.
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What is the correct answer to this question?
\(16a^2-25b^2\)
Why is this the correct answer?
\(16a^2-25b^2=(4a)^2-(5b)^2\) is a difference of two squares. Using \(p^2-q^2=(p+q)(p-q)\), it factorises as \((4a+5b)(4a-5b)\), a pair of conjugate binomials. Option C factorises as \((4a-5b)^2\); its two binomials are identical, not conjugates. Exam tip: look for a minus sign between two perfect-square terms when identifying conjugate factors.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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