Write \(x^2-16=0\) in factorised (factor) form.
Answer and explanation
Correct answer: \((x-4)(x+4)=0\)
\(x^2-16\) is a difference of squares since \(16=4^2\). Use the identity \(a^2-b^2=(a-b)(a+b)\) with \(a=x\) and \(b=4\) to get \((x-4)(x+4)=0\). The other choices give different middle terms when expanded; for example \((x-4)^2\) yields a \(-8x\) term, so it does not match the original expression. Exam tip: spot the difference-of-squares pattern or expand candidate factors to check coefficients quickly.
Frequently asked questions
What is the correct answer to this question?
\((x-4)(x+4)=0\)
Why is this the correct answer?
\(x^2-16\) is a difference of squares since \(16=4^2\). Use the identity \(a^2-b^2=(a-b)(a+b)\) with \(a=x\) and \(b=4\) to get \((x-4)(x+4)=0\). The other choices give different middle terms when expanded; for example \((x-4)^2\) yields a \(-8x\) term, so it does not match the original expression. Exam tip: spot the difference-of-squares pattern or expand candidate factors to check coefficients quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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