What will be the factorised form of \(y^2+12y+36\)?
Answer and explanation
Correct answer: \((y+6)^2\)
The expression \(y^2+12y+36\) matches the identity \(a^2+2ab+b^2=(a+b)^2\). Taking \(a=y\) and \(b=6\), we get \(2ab=2\times y\times6=12y\) and \(b^2=36\). Hence, its factorised form is \((y+6)^2\). Expanding \((y-6)^2\) gives a middle term of \(-12y\), so it is not correct. Exam tip: for a perfect-square trinomial, use the square root of the constant term and choose the bracket sign from the middle term.
Frequently asked questions
What is the correct answer to this question?
\((y+6)^2\)
Why is this the correct answer?
The expression \(y^2+12y+36\) matches the identity \(a^2+2ab+b^2=(a+b)^2\). Taking \(a=y\) and \(b=6\), we get \(2ab=2\times y\times6=12y\) and \(b^2=36\). Hence, its factorised form is \((y+6)^2\). Expanding \((y-6)^2\) gives a middle term of \(-12y\), so it is not correct. Exam tip: for a perfect-square trinomial, use the square root of the constant term and choose the bracket sign from the middle term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
