Which of the following expressions can be identified and factorised as a difference of two perfect squares?
Answer and explanation
Correct answer: \(49a^2-64b^2\)
In option A, \(49a^2=(7a)^2\) and \(64b^2=(8b)^2\). Thus, \(49a^2-64b^2=(7a)^2-(8b)^2\), which is a difference of two perfect squares. Its factorisation is \((7a-8b)(7a+8b)\). Option B is a sum of squares, while in options C and D the second term is not a perfect square. Exam tip: before using \(x^2-y^2=(x-y)(x+y)\), verify that both terms are perfect squares.
Frequently asked questions
What is the correct answer to this question?
\(49a^2-64b^2\)
Why is this the correct answer?
In option A, \(49a^2=(7a)^2\) and \(64b^2=(8b)^2\). Thus, \(49a^2-64b^2=(7a)^2-(8b)^2\), which is a difference of two perfect squares. Its factorisation is \((7a-8b)(7a+8b)\). Option B is a sum of squares, while in options C and D the second term is not a perfect square. Exam tip: before using \(x^2-y^2=(x-y)(x+y)\), verify that both terms are perfect squares.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
