Rewrite the equation with the squared brackets as two separate brackets.

$(x + 1) (x - 3) (x - 3)$

Expand the first two brackets by multiplying everything in the first bracket by everything in the second bracket.

$\begin{array}{rcl} (x + 1) (x - 3) \\ = & x (x - 3) + 1 (x - 3) \\ = & x^{2} - 3 x + 1 x - 3 \end{array}$

[1]

Simplify this.

$\begin{array}{rcl} x^{2} - 3 x + 1 x - 3 & = & x^{2} - 2 x - 3 \end{array}$

Write the expanded expression out next to the third bracket.

$\begin{array}{rcl} (\begin{array}{rcl} x^{2} - 2 x - 3 \end{array}) (x - 3) \end{array}$

Multiply each part of the first bracket by $(x - 3)$ .

$\begin{array}{rcl} x^{2} (x - 3) - 2 x (x - 3) - 3 (x - 3) \end{array}$

Expand the brackets, taking extra care with the negatives.

$\begin{array}{l} x^{3} - 3 x^{2} - 2 x^{2} + 6 x - 3 x - (- 9) \end{array}$

[1]

Simplify, taking extra care with the negatives.

$\begin{array}{l} x^{3} - 5 x^{2} + 3 x + 9 \end{array}$ [1]
This could be done by expanding (x -3)²first.

Expanding & Factorising Brackets (CIE IGCSE Maths: Extended)

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