Which of the following is equal to the expression \(x^2+14x+49\)?
Answer and explanation
Correct answer: \((x+7)^2\)
Use the perfect-square identity \((a+b)^2=a^2+2ab+b^2\). Taking \(a=x\) and \(b=7\), we get \((x+7)^2=x^2+2\cdot x\cdot7+7^2=x^2+14x+49\), so option A is correct. Option B would produce the middle term \(-14x\), not \(+14x\). Exam tip: take the square root of the constant term and use the sign of the middle term to choose the appropriate binomial.
Frequently asked questions
What is the correct answer to this question?
\((x+7)^2\)
Why is this the correct answer?
Use the perfect-square identity \((a+b)^2=a^2+2ab+b^2\). Taking \(a=x\) and \(b=7\), we get \((x+7)^2=x^2+2\cdot x\cdot7+7^2=x^2+14x+49\), so option A is correct. Option B would produce the middle term \(-14x\), not \(+14x\). Exam tip: take the square root of the constant term and use the sign of the middle term to choose the appropriate binomial.
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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