\( 25m^2-70mn+49n^2 \) is the square of what?
Answer and explanation
Correct answer: \((5m-7n)^2\)
The first term is \(25m^2=(5m)^2\), and the last term is \(49n^2=(7n)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=5m\) and \(b=7n\), the middle term becomes \(-2(5m)(7n)=-70mn\). Hence the expression is \((5m-7n)^2\). In contrast, \((5m+7n)^2\) would have the positive middle term \(+70mn\). Exam tip: while identifying a perfect square, always check the sign of the middle term and verify \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\((5m-7n)^2\)
Why is this the correct answer?
The first term is \(25m^2=(5m)^2\), and the last term is \(49n^2=(7n)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=5m\) and \(b=7n\), the middle term becomes \(-2(5m)(7n)=-70mn\). Hence the expression is \((5m-7n)^2\). In contrast, \((5m+7n)^2\) would have the positive middle term \(+70mn\). Exam tip: while identifying a perfect square, always check the sign of the middle term and verify \(2ab\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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