Which of the following trinomials can be factorised into the product of two identical binomials?
Answer and explanation
Correct answer: \(x^2-10x+25\)
In a perfect-square trinomial, the middle term must match \(2abx\) and the constant must be \(b^2\). Here, \(-10x=2(x)(-5)\) and \(25=(-5)^2\), so \(x^2-10x+25=(x-5)^2\). In option B, 20 is not a perfect square. Exam tip: check the square root of the constant against the middle term.
Frequently asked questions
What is the correct answer to this question?
\(x^2-10x+25\)
Why is this the correct answer?
In a perfect-square trinomial, the middle term must match \(2abx\) and the constant must be \(b^2\). Here, \(-10x=2(x)(-5)\) and \(25=(-5)^2\), so \(x^2-10x+25=(x-5)^2\). In option B, 20 is not a perfect square. Exam tip: check the square root of the constant against the middle term.
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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