Mathematics

Expansion

Q: Which of the following expressions is in expanded form?

\(5m-7\) In \(5m-7\), there is no bracket, power of a binomial, or outside factor left to distribute, so it is already in expanded form. The expressions \(3(x+2)\) and \(x(y+4)\) can be expanded using the distributive property, while \((a+b)^2\) can also be expanded. Exam tip: An expanded expression is usually written as separate terms with no brackets left to multiply out.

Q: What is the correct expansion of the expression 3(a − 2)?

3a − 6 Using the distributive property, multiply 3 by each term inside the bracket: 3 × a + 3 × (−2) = 3a − 6. Therefore, option A is correct. In option B, 3 has not been multiplied by −2, while option D incorrectly changes the negative sign to a positive sign. Exam tip: when expanding a bracket, multiply the outside factor by every term inside it.

Expansion in Class 9 Mathematics explains how to open brackets and rewrite algebraic expressions in simplified form. Students learn to use the distributive property, combine like terms, and apply familiar algebraic identities when multiplying terms or expressions. The topic also helps them recognise common errors, maintain correct signs, and check whether two expanded forms are equivalent. It addresses common questions about the steps, notation, and reasoning used in algebraic expansion.

Easy · Level 1 · 2 questions

Practice questions

01Which of the following expressions is in expanded form?

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Answer and explanation

Correct answer: C. \(5m-7\)

In \(5m-7\), there is no bracket, power of a binomial, or outside factor left to distribute, so it is already in expanded form. The expressions \(3(x+2)\) and \(x(y+4)\) can be expanded using the distributive property, while \((a+b)^2\) can also be expanded. Exam tip: An expanded expression is usually written as separate terms with no brackets left to multiply out.

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02What is the correct expansion of the expression 3(a − 2)?

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Answer and explanation

Correct answer: A. 3a − 6

Using the distributive property, multiply 3 by each term inside the bracket: 3 × a + 3 × (−2) = 3a − 6. Therefore, option A is correct. In option B, 3 has not been multiplied by −2, while option D incorrectly changes the negative sign to a positive sign. Exam tip: when expanding a bracket, multiply the outside factor by every term inside it.