What is the coefficient of the term containing (a^2b) in ( (3a-b)^3 )?
Answer and explanation
Correct answer: (-27)
To find the coefficient of the term containing \\(a^2b\\) in \\((3a-b)^3\\), use the cube-of-a-difference identity \\((x-y)^3=x^3-3x^2y+3xy^2-y^3\\). Here, take \\(x=3a\\) and \\(y=b\\). The second term is \\(-3(3a)^2b\\), which becomes \\(-3\cdot9a^2b=-27a^2b\\). Thus the required coefficient is \\(-27\\), including its negative sign.
Hence option B follows. A common error is to calculate only \\(3(3a)^2b=27a^2b\\) and forget that the middle term has a minus sign. Option A gives the first term’s coefficient, not the coefficient of \\(a^2b\\). Options C and D result from incorrect multiplication or an incorrect sign. The complete expansion confirms the answer.
Frequently asked questions
What is the correct answer to this question?
(-27)
Why is this the correct answer?
To find the coefficient of the term containing \\(a^2b\\) in \\((3a-b)^3\\), use the cube-of-a-difference identity \\((x-y)^3=x^3-3x^2y+3xy^2-y^3\\). Here, take \\(x=3a\\) and \\(y=b\\). The second term is \\(-3(3a)^2b\\), which becomes \\(-3\cdot9a^2b=-27a^2b\\). Thus the required coefficient is \\(-27\\), including its negative sign.
Hence option B follows. A common error is to calculate only \\(3(3a)^2b=27a^2b\\) and forget that the middle term has a minus sign. Option A gives the first term’s coefficient, not the coefficient of \\(a^2b\\). Options C and D result from incorrect multiplication or an incorrect sign. The complete expansion confirms the answer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
