Which is the factorised form of (9x^2+24xy+16y^2)?
Answer and explanation
Correct answer: ((3x+4y)^2)
This trinomial has the pattern of a perfect square: the first term is \((3x)^2\), the last term is \((4y)^2\), and the middle term should be twice their product. Twice the product is \(2(3x)(4y)=24xy\), exactly the middle term given. Therefore the identity \(a^2+2ab+b^2=(a+b)^2\) can be used directly.
Taking \(a=3x\) and \(b=4y\), the expression becomes \((3x+4y)^2\). Expanding gives \(9x^2+24xy+16y^2\), so option A matches every term. Option B would create a negative middle term, and option C uses incorrect square roots. The product form in option D gives different middle terms.
Frequently asked questions
What is the correct answer to this question?
((3x+4y)^2)
Why is this the correct answer?
This trinomial has the pattern of a perfect square: the first term is \((3x)^2\), the last term is \((4y)^2\), and the middle term should be twice their product. Twice the product is \(2(3x)(4y)=24xy\), exactly the middle term given. Therefore the identity \(a^2+2ab+b^2=(a+b)^2\) can be used directly.
Taking \(a=3x\) and \(b=4y\), the expression becomes \((3x+4y)^2\). Expanding gives \(9x^2+24xy+16y^2\), so option A matches every term. Option B would create a negative middle term, and option C uses incorrect square roots. The product form in option D gives different middle terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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