What will be the factorised form of (r^2 - 2rs + s^2)?
Answer and explanation
Correct answer: (r - s)^2
The governing identity is the square of a difference: a² − 2ab + b² = (a − b)². Match the given expression with this pattern by taking a = r and b = s. The first term r² matches a², the middle term −2rs matches −2ab, and the final term s² matches b². Therefore r² − 2rs + s² = (r−s)², so option B is correct. Expanding the selected factorisation gives r² − rs − rs + s² = r² − 2rs + s², confirming it exactly. Option A has a positive middle term, option C gives the difference of squares r²−s², and option D produces different coefficients and terms. The signs and the middle coefficient are decisive in this factorisation.
Frequently asked questions
What is the correct answer to this question?
(r - s)^2
Why is this the correct answer?
The governing identity is the square of a difference: a² − 2ab + b² = (a − b)². Match the given expression with this pattern by taking a = r and b = s. The first term r² matches a², the middle term −2rs matches −2ab, and the final term s² matches b². Therefore r² − 2rs + s² = (r−s)², so option B is correct. Expanding the selected factorisation gives r² − rs − rs + s² = r² − 2rs + s², confirming it exactly. Option A has a positive middle term, option C gives the difference of squares r²−s², and option D produces different coefficients and terms. The signs and the middle coefficient are decisive in this factorisation.
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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