What is the full expansion of ( (x+1)(x+2)(x+3) )?
Answer and explanation
Correct answer: \(x^3+6x^2+11x+6\)
First, \((x+1)(x+2)=x^2+3x+2\). Multiplying this by \((x+3)\) gives \(x^3+3x^2+3x^2+9x+2x+6=x^3+6x^2+11x+6\). Hence, option A is correct. In option B, the coefficient of \(x^2\) is incorrectly written as 5 instead of 6. Exam tip: combine like terms carefully after multiplication.
Frequently asked questions
What is the correct answer to this question?
\(x^3+6x^2+11x+6\)
Why is this the correct answer?
First, \((x+1)(x+2)=x^2+3x+2\). Multiplying this by \((x+3)\) gives \(x^3+3x^2+3x^2+9x+2x+6=x^3+6x^2+11x+6\). Hence, option A is correct. In option B, the coefficient of \(x^2\) is incorrectly written as 5 instead of 6. Exam tip: combine like terms carefully after multiplication.
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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