IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1Revision NotesAlgebraExpanding BracketsExpanding Triple Brackets

Expanding Triple Brackets (Edexcel IGCSE Maths A (Modular))

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Author

Mark Curtis

Expertise

Maths

Expanding Three Brackets

How do I expand three brackets?

Multiply out any two of the brackets using a standard method and simplify
Then multiply the resulting expression by the third (unused) bracket

This step often looks like (x + a)(x² + bx + c)
Every term in the first bracket must be multiplied with every term in the second bracket
A grid can help to keep track of all the terms
- E.g. (x + 2)(x² + 3x + 1)
  x²
  +3x
  +1
  x
  x³
  3x²
  x
  +2
  2x²
  6x
  2

	x²	+3x	+1
x	x³	3x²	x
+2	2x²	6x	2

Add all the terms inside the grid together
- x³ + 2x²+ 3x² + 6x + x + 2
Simplify by collecting any like terms
- x³ + 5x² + 7x + 2

Worked Example

Expand $(2 x - 3) (x + 4) (3 x - 1)$ .

Expand and simplify the first two brackets, for example using the FOIL method

$\begin{array}{rcl} (2 x - 3) (x + 4) \\ = & 2 x \times x + 2 x \times 4 + (- 3) \times x + (- 3) \times 4 \\ = & 2 x^{2} + 8 x - 3 x - 12 \\ = & 2 x^{2} + 5 x - 12 \end{array}$

Rewrite the original expression with the first two brackets expanded

$(2 x^{2} + 5 x - 12) (3 x - 1)$

Multiply all of the terms in the first set of brackets by all of the terms in the second set of brackets

A grid can help when there are many terms to multiply together (e.g. write $2 x^{2} + 5 x - 12$ in the vertical column and $3 x - 1$ in the horizontal column, then multiply corresponding terms)

	$3 x$	$- 1$
$2 x^{2}$	$6 x^{3}$	$- 2 x^{2}$
$5 x$	$15 x^{2}$	$- 5 x$
$- 12$	$- 36 x$	$12$

Write out the multiplied terms

$6 x^{3} - 2 x^{2} + 15 x^{2} - 5 x - 36 + 12$

Collect the like terms to simplify

$6 x^{3} + 13 x^{2} - 41 x + 12$

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Author: Mark Curtis

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.