Choose the correct coefficient of (a^2b) in ( (2a+b)^3 ).
Answer and explanation
Correct answer: 12
Use the identity
a+b)^3=a^3+3a^2b+3ab^2+b^3
a-b)^3=a^3-3a^2b+3ab^2-b^3
with the first term equal to 2a. Thus,
(2a+b)^3=(2a)^3+3(2a)^2b+3(2a)b^2+b^3
=8a^3+12a^2b+6ab^2+b^3.
Therefore, the coefficient of a^2b is 12. The value 6 is the coefficient of ab^2, so it is a close but incorrect distractor. Exam tip: while finding a coefficient, include the numerical factor raised to the required power.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Use the identity
a+b)^3=a^3+3a^2b+3ab^2+b^3
a-b)^3=a^3-3a^2b+3ab^2-b^3
with the first term equal to 2a. Thus,
(2a+b)^3=(2a)^3+3(2a)^2b+3(2a)b^2+b^3
=8a^3+12a^2b+6ab^2+b^3.
Therefore, the coefficient of a^2b is 12. The value 6 is the coefficient of ab^2, so it is a close but incorrect distractor. Exam tip: while finding a coefficient, include the numerical factor raised to the required power.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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