Which of the following expresses \(x^2+10x+25=0\) in factorised (product) form?
Answer and explanation
Correct answer: \((x+5)^2=0\)
\(x^2+10x+25\) is a perfect square trinomial of the form \((a+b)^2=a^2+2ab+b^2\). Taking \(a=x\) and \(b=5\) gives \((x+5)^2=x^2+2\cdot x\cdot5+5^2=x^2+10x+25\), so the factorised form is \((x+5)^2=0\). The closest distractor \((x-5)^2\) is incorrect because \((x-5)^2=x^2-10x+25\), which has \(-10x\) instead of \(+10x\). Exam tip: compare the middle term with \(2ab\) and check the sign to identify the correct binomial square.
Frequently asked questions
What is the correct answer to this question?
\((x+5)^2=0\)
Why is this the correct answer?
\(x^2+10x+25\) is a perfect square trinomial of the form \((a+b)^2=a^2+2ab+b^2\). Taking \(a=x\) and \(b=5\) gives \((x+5)^2=x^2+2\cdot x\cdot5+5^2=x^2+10x+25\), so the factorised form is \((x+5)^2=0\). The closest distractor \((x-5)^2\) is incorrect because \((x-5)^2=x^2-10x+25\), which has \(-10x\) instead of \(+10x\). Exam tip: compare the middle term with \(2ab\) and check the sign to identify the correct binomial square.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
