What is the simplest factorised form of (12x^2y-18xy^2)?
Answer and explanation
Correct answer: (6xy(2x-3y))
The governing concept is factorisation by taking out the greatest common factor. For 12x²y and 18xy², the greatest common numerical factor is 6. Both terms contain x and y, so the greatest common monomial factor is 6xy. Dividing the first term by 6xy gives 2x, and dividing the second term by 6xy gives 3y. The original minus sign must remain, so the result is 6xy(2x−3y). Option B is algebraically equivalent after further factorisation, but it has not taken out the greatest common factor. Option C also leaves a common factor inside, while D changes subtraction into addition. Hence option A is the simplest correct form.
Frequently asked questions
What is the correct answer to this question?
(6xy(2x-3y))
Why is this the correct answer?
The governing concept is factorisation by taking out the greatest common factor. For 12x²y and 18xy², the greatest common numerical factor is 6. Both terms contain x and y, so the greatest common monomial factor is 6xy. Dividing the first term by 6xy gives 2x, and dividing the second term by 6xy gives 3y. The original minus sign must remain, so the result is 6xy(2x−3y). Option B is algebraically equivalent after further factorisation, but it has not taken out the greatest common factor. Option C also leaves a common factor inside, while D changes subtraction into addition. Hence option A is the simplest correct form.
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.
