Factorise (9a^2-25b^2).
Answer and explanation
Correct answer: \((3a-5b)(3a+5b)\)
This is a difference of squares because \(9a^2=(3a)^2\) and \(25b^2=(5b)^2\). Applying \(x^2-y^2=(x-y)(x+y)\) with \(x=3a\) and \(y=5b\) gives \((3a-5b)(3a+5b)\). Option A expands to \(9a^2-30ab+25b^2\), so it does not match the given expression. Exam tip: for a difference of squares, write the difference and sum of the two square roots as factors.
Frequently asked questions
What is the correct answer to this question?
\((3a-5b)(3a+5b)\)
Why is this the correct answer?
This is a difference of squares because \(9a^2=(3a)^2\) and \(25b^2=(5b)^2\). Applying \(x^2-y^2=(x-y)(x+y)\) with \(x=3a\) and \(y=5b\) gives \((3a-5b)(3a+5b)\). Option A expands to \(9a^2-30ab+25b^2\), so it does not match the given expression. Exam tip: for a difference of squares, write the difference and sum of the two square roots as 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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