Which is the factorised form of (2xy + 6y + 5x + 15)?
Answer and explanation
Correct answer: (2y + 5)(x + 3)
The governing method is factorisation by grouping. Group terms that share useful common factors: 2xy + 6y + 5x + 15 = (2xy+6y) + (5x+15). Factoring each group gives 2y(x+3) + 5(x+3). Both terms now contain the common binomial x+3, so taking it outside produces (2y+5)(x+3). Therefore option A is correct. Expansion verifies the result: (2y+5)(x+3) = 2xy + 6y + 5x + 15. Option B changes the signs of the 5x and constant terms. Option C pairs the variables incorrectly and does not recreate the original expression, while option D gives unrelated products. Grouping is effective because it creates the same binomial factor in both groups.
Frequently asked questions
What is the correct answer to this question?
(2y + 5)(x + 3)
Why is this the correct answer?
The governing method is factorisation by grouping. Group terms that share useful common factors: 2xy + 6y + 5x + 15 = (2xy+6y) + (5x+15). Factoring each group gives 2y(x+3) + 5(x+3). Both terms now contain the common binomial x+3, so taking it outside produces (2y+5)(x+3). Therefore option A is correct. Expansion verifies the result: (2y+5)(x+3) = 2xy + 6y + 5x + 15. Option B changes the signs of the 5x and constant terms. Option C pairs the variables incorrectly and does not recreate the original expression, while option D gives unrelated products. Grouping is effective because it creates the same binomial factor 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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