A student claims that the factorisation of \(49a^2-64b^2\) is \((7a-8b)^2\). What is the error in the student's claim?
Answer and explanation
Correct answer: यह दो वर्गों का अंतर है, इसलिए सही गुणनखंड \((7a-8b)(7a+8b)\) है।
Here \(49a^2=(7a)^2\) and \(64b^2=(8b)^2\). Using \(x^2-y^2=(x-y)(x+y)\) gives \((7a-8b)(7a+8b)\). Squaring \((7a-8b)\) would also produce \(-112ab\), which is absent. Exam tip: for a difference of squares, use conjugate factors.
Frequently asked questions
What is the correct answer to this question?
यह दो वर्गों का अंतर है, इसलिए सही गुणनखंड \((7a-8b)(7a+8b)\) है।
Why is this the correct answer?
Here \(49a^2=(7a)^2\) and \(64b^2=(8b)^2\). Using \(x^2-y^2=(x-y)(x+y)\) gives \((7a-8b)(7a+8b)\). Squaring \((7a-8b)\) would also produce \(-112ab\), which is absent. Exam tip: for a difference of squares, use 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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