Which of the following expressions can be written as a product of two binomials?
Answer and explanation
Correct answer: \(x^2-16\)
\(x^2-16=x^2-4^2\) is a difference of two perfect squares. Using \(a^2-b^2=(a-b)(a+b)\), we get \(x^2-16=(x-4)(x+4)\); hence it is a product of two binomials. In contrast, \(x^2+8x+17=(x+4)^2+1\), so it cannot be factorised into two binomials with real coefficients. Exam tip: for a difference of squares, check that both terms are perfect squares and that there is a minus sign between them.
Frequently asked questions
What is the correct answer to this question?
\(x^2-16\)
Why is this the correct answer?
\(x^2-16=x^2-4^2\) is a difference of two perfect squares. Using \(a^2-b^2=(a-b)(a+b)\), we get \(x^2-16=(x-4)(x+4)\); hence it is a product of two binomials. In contrast, \(x^2+8x+17=(x+4)^2+1\), so it cannot be factorised into two binomials with real coefficients. Exam tip: for a difference of squares, check that both terms are perfect squares and that there is a minus sign between them.
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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