Expanding & Simplifying Single Brackets (Edexcel IGCSE Maths A (Modular))

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Expanding One Bracket

How do I expand a bracket?

  • The expression 3x (x + 2) means 3x  multiplied by the bracket (x + 2)

    • 3is the term outside the bracket

      • this is sometimes called a factor

    • and x + 2 are the terms inside the bracket

  • Expanding the brackets means multiplying the outside term by each term on the inside

    • This will remove (get rid of) the brackets

    • 3x (x + 2) expands to 3 x cross times x plus 3 x cross times 2 which simplifies to 3 x squared plus 6 x

  • Beware of minus signs

    • Remember the rules
      −  ×  −  =  +
      −  ×  +  =  − 

    • It helps to put brackets around negative terms

Worked Example

(a) Expand  4 x open parentheses 2 x minus 3 close parentheses.

 Multiply the 4 x term outside the brackets by both terms inside the brackets

4 x cross times 2 x plus 4 x cross times open parentheses negative 3 close parentheses

Simplify

bold 8 bold italic x to the power of bold 2 bold minus bold 12 bold italic x

(b) Expand  negative 7 x open parentheses 4 minus 5 y close parentheses.

Multiply the negative 7 x outside the brackets by both terms inside the brackets

open parentheses negative 7 x close parentheses cross times 4 plus open parentheses negative 7 x close parentheses cross times open parentheses negative 5 y close parentheses

Simplify and remember that multiplying two negatives gives a positive

bold minus bold 28 bold italic x bold plus bold 35 bold italic x bold italic y

Expand & Simplify

How do I simplify brackets that are added together?

  • First expand both brackets separately

    • 4 open parentheses x plus 7 close parentheses plus 5 x open parentheses 3 minus x close parentheses 

      • The first set of brackets expands to 4 cross times x plus 4 cross times 7 which simplifies to 4 x plus 28

      • The second set of brackets expands to 5 x cross times 3 plus 5 x cross times open parentheses negative x close parentheses which simplifies to 15 x minus 5 x squared

      • So 4 open parentheses x plus 7 close parentheses plus 5 x open parentheses 3 minus x close parentheses equals 4 x plus 28 plus 15 x minus 5 x squared

  • Then collect like terms

    • 4 x plus 15 x equals 19 x

      • The other two terms are not like terms

    • So 4 open parentheses x plus 7 close parentheses plus 5 x open parentheses 3 minus x close parentheses equals 19 x plus 28 minus 5 x squared 

Worked Example

(a) Expand and simplify  2 open parentheses x plus 5 close parentheses plus 3 x open parentheses x minus 8 close parentheses.

Expand each set of brackets separately

You can keep negative terms inside brackets

2 cross times x plus 2 cross times 5 plus 3 x cross times x plus 3 x cross times open parentheses negative 8 close parentheses

Simplify each term

2 x plus 10 plus 3 x squared minus 24 x

Collect like terms (the 2x and the -24x)

bold minus bold 22 bold italic x bold plus bold 10 bold plus bold 3 bold italic x to the power of bold 2

(b) Expand and simplify  3 x open parentheses x plus 2 close parentheses minus 7 open parentheses x minus 6 close parentheses.

Expand each set of brackets separately
Be careful: the second set of brackets has a -7 in front, not +7

 3 x cross times x plus 3 x cross times 2 plus open parentheses negative 7 close parentheses cross times x plus open parentheses negative 7 close parentheses cross times open parentheses negative 6 close parentheses

Simplify each term
Remember that multiplying two negatives gives a positive

3 x squared plus 6 x minus 7 x plus 42

Collect like terms

bold 3 bold italic x to the power of bold 2 bold minus bold italic x bold plus bold 42

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Mark Curtis

Author: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.