Which of the following trinomials is a perfect-square trinomial that can be factorised as the product of two identical binomials?
Answer and explanation
Correct answer: \(x^2+8x+16\)
\(x^2+8x+16=x^2+2\cdot x\cdot4+4^2=(x+4)^2=(x+4)(x+4)\). Hence, it is the product of two identical binomials. In option C, since \(16=4^2\), the middle term should be \(2\cdot x\cdot4=8x\), not \(6x\). Exam tip: use \(a^2+2ab+b^2=(a+b)^2\) to check the middle term.
Frequently asked questions
What is the correct answer to this question?
\(x^2+8x+16\)
Why is this the correct answer?
\(x^2+8x+16=x^2+2\cdot x\cdot4+4^2=(x+4)^2=(x+4)(x+4)\). Hence, it is the product of two identical binomials. In option C, since \(16=4^2\), the middle term should be \(2\cdot x\cdot4=8x\), not \(6x\). Exam tip: use \(a^2+2ab+b^2=(a+b)^2\) to check 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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