How will (m^2-10m+25) be written in factorised form?
Answer and explanation
Correct answer: ((m-5)^2)
The expression has the standard perfect-square form \(a^2-2ab+b^2\). The first term \(m^2\) is the square of m, while the last term 25 is the square of 5. To check the middle term, calculate \(-2(m)(5)=-10m\). This agrees exactly with the given expression. Therefore, the two quantities are m and 5, with a minus sign between them.
Applying the identity gives \(m^2-10m+25=(m-5)^2\). On expanding, \((m-5)^2=m^2-5m-5m+25=m^2-10m+25\), so the factorisation is verified. Hence option B is correct. Option A would give a positive middle term, \(+10m\), and options C and D do not reproduce the original three terms when expanded.
Frequently asked questions
What is the correct answer to this question?
((m-5)^2)
Why is this the correct answer?
The expression has the standard perfect-square form \(a^2-2ab+b^2\). The first term \(m^2\) is the square of m, while the last term 25 is the square of 5. To check the middle term, calculate \(-2(m)(5)=-10m\). This agrees exactly with the given expression. Therefore, the two quantities are m and 5, with a minus sign between them.
Applying the identity gives \(m^2-10m+25=(m-5)^2\). On expanding, \((m-5)^2=m^2-5m-5m+25=m^2-10m+25\), so the factorisation is verified. Hence option B is correct. Option A would give a positive middle term, \(+10m\), and options C and D do not reproduce the original three terms when expanded.
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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