Which of the following is equal to the expression \(x^2-16x+64\)?
Answer and explanation
Correct answer: \((x-8)^2\)
The expression can be written as \(x^2-2\cdot x\cdot 8+8^2\). Using \(a^2-2ab+b^2=(a-b)^2\), it equals \((x-8)^2\). Option B would produce a middle term of \(+16x\), so it is incorrect. Exam tip: identify the square roots of the first and last terms, then check whether the middle term is \(-2ab\) or \(+2ab\).
Frequently asked questions
What is the correct answer to this question?
\((x-8)^2\)
Why is this the correct answer?
The expression can be written as \(x^2-2\cdot x\cdot 8+8^2\). Using \(a^2-2ab+b^2=(a-b)^2\), it equals \((x-8)^2\). Option B would produce a middle term of \(+16x\), so it is incorrect. Exam tip: identify the square roots of the first and last terms, then check whether the middle term is \(-2ab\) or \(+2ab\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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