Which of the following expressions is a perfect-square trinomial that can be written as the square of a binomial?
Answer and explanation
Correct answer: \(9a^2-24ab+16b^2\)
A perfect-square trinomial has the form \(x^2-2xy+y^2=(x-y)^2\). Here, \(9a^2=(3a)^2\), \(16b^2=(4b)^2\), and the middle term is \(-24ab=-2(3a)(4b)\). Hence, \(9a^2-24ab+16b^2=(3a-4b)^2\). In option B, the last term is \(15b^2\), but it must be \(16b^2=(4b)^2\). Exam tip: take the square roots of the first and last terms and check whether the middle term is \(\pm2\) times their product.
Frequently asked questions
What is the correct answer to this question?
\(9a^2-24ab+16b^2\)
Why is this the correct answer?
A perfect-square trinomial has the form \(x^2-2xy+y^2=(x-y)^2\). Here, \(9a^2=(3a)^2\), \(16b^2=(4b)^2\), and the middle term is \(-24ab=-2(3a)(4b)\). Hence, \(9a^2-24ab+16b^2=(3a-4b)^2\). In option B, the last term is \(15b^2\), but it must be \(16b^2=(4b)^2\). Exam tip: take the square roots of the first and last terms and check whether the middle term is \(\pm2\) times their product.
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.
