Choose the correct factorisation of (25r^2-30r+9).
Answer and explanation
Correct answer: \((5r-3)^2\)
The expression is a perfect-square trinomial: \(25r^2=(5r)^2\) and \(9=3^2\). Also, \(-30r=-2\times 5r\times 3\). Using \(a^2-2ab+b^2=(a-b)^2\), with \(a=5r\) and \(b=3\), we get \(25r^2-30r+9=(5r-3)^2\). In option A, the middle term would be \(+30r\). Exam tip: take the square roots of the first and last terms, then verify the middle term using \(\pm2ab\).
Frequently asked questions
What is the correct answer to this question?
\((5r-3)^2\)
Why is this the correct answer?
The expression is a perfect-square trinomial: \(25r^2=(5r)^2\) and \(9=3^2\). Also, \(-30r=-2\times 5r\times 3\). Using \(a^2-2ab+b^2=(a-b)^2\), with \(a=5r\) and \(b=3\), we get \(25r^2-30r+9=(5r-3)^2\). In option A, the middle term would be \(+30r\). Exam tip: take the square roots of the first and last terms, then verify the middle term using \(\pm2ab\).
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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