What is the factorisation of (2xy+6x+5y+15)?
Answer and explanation
Correct answer: ( (2x+5)(y+3) )
The expression can be factorised by grouping terms that produce the same bracket. The first two terms contain 2x, and the last two contain 5. After grouping, the expression becomes 2x(y+3)+5(y+3). Both terms now contain the common factor (y+3), so it can be taken outside. The remaining factor is (2x+5), giving (2x+5)(y+3). This is option A.
To verify the result, multiply: (2x+5)(y+3)=2xy+6x+5y+15, exactly the original expression. Option B would give different coefficients, while the other options also produce incorrect signs or terms. The key method is to arrange terms so that the same bracket appears in both groups.
Frequently asked questions
What is the correct answer to this question?
( (2x+5)(y+3) )
Why is this the correct answer?
The expression can be factorised by grouping terms that produce the same bracket. The first two terms contain 2x, and the last two contain 5. After grouping, the expression becomes 2x(y+3)+5(y+3). Both terms now contain the common factor (y+3), so it can be taken outside. The remaining factor is (2x+5), giving (2x+5)(y+3). This is option A.
To verify the result, multiply: (2x+5)(y+3)=2xy+6x+5y+15, exactly the original expression. Option B would give different coefficients, while the other options also produce incorrect signs or terms. The key method is to arrange terms so that the same bracket appears in both groups.
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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