What is the expansion of ( (x+2)^3 )?
Answer and explanation
Correct answer: \(x^3+6x^2+12x+8\)
Using \((a+b)^3=a^3+3a^2b+3ab^2+b^3\), put \(a=x\) and \(b=2\). Thus, \((x+2)^3=x^3+3x^2(2)+3x(2^2)+2^3=x^3+6x^2+12x+8\). In option B, the coefficients of the middle terms are incorrect, while option C omits both middle terms. Exam tip: in a cube expansion, always include both middle terms, \(3a^2b\) and \(3ab^2\).
Frequently asked questions
What is the correct answer to this question?
\(x^3+6x^2+12x+8\)
Why is this the correct answer?
Using \((a+b)^3=a^3+3a^2b+3ab^2+b^3\), put \(a=x\) and \(b=2\). Thus, \((x+2)^3=x^3+3x^2(2)+3x(2^2)+2^3=x^3+6x^2+12x+8\). In option B, the coefficients of the middle terms are incorrect, while option C omits both middle terms. Exam tip: in a cube expansion, always include both middle terms, \(3a^2b\) and \(3ab^2\).
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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