Which of the following trinomials is a perfect-square trinomial that can be written as the product of two identical binomials?
Answer and explanation
Correct answer: \(x^2+6x+9\)
In \(x^2+6x+9\), \(x^2=(x)^2\), \(9=3^2\), and the middle term is \(6x=2\times x\times3\). Therefore, \(x^2+6x+9=(x+3)^2=(x+3)(x+3)\), so option A is correct. In option B, \(8\) is not \(3^2\), so it cannot equal \((x+3)^2\). Exam tip: for a perfect-square trinomial, check whether the middle term is twice the product of the square roots of the first and last terms.
Frequently asked questions
What is the correct answer to this question?
\(x^2+6x+9\)
Why is this the correct answer?
In \(x^2+6x+9\), \(x^2=(x)^2\), \(9=3^2\), and the middle term is \(6x=2\times x\times3\). Therefore, \(x^2+6x+9=(x+3)^2=(x+3)(x+3)\), so option A is correct. In option B, \(8\) is not \(3^2\), so it cannot equal \((x+3)^2\). Exam tip: for a perfect-square trinomial, check whether the middle term is twice the product of the square roots of the first and last terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
