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Chapter overview

Learning goals

**Learning Goals**

- Understand how to multiply double and triple brackets

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Double brackets consist of two binomial expressions multiplied together, e.g. $(x+1)(y-3)$, whereas triple brackets consist of three binomial expressions multiplied together, e.g. $(x-2)(x+6)(x+9)$. The principle behind multiplying out double brackets can be extended to multiplying out triple brackets, using the FOIL method, or a multiplication grid.

You can expand two pairs of brackets by multiplying each term in the first set of brackets by each term in he second set. This can be done by using a multiplication grid.

*Expand the brackets* $(x+1)(2x-3)$

*Fill in the multiplication grid*

$\times$ | $\boldsymbol{x}$ | $\bold{+1}$ |

$\boldsymbol{2x}$ | $2x^2$ | $+2x$ |

$\bold{-3}$ | $-3x$ | $-3$ |

*Add and simplify the results*

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

*Note:** when there are just two binomial expressions, you can also use the **FOIL** method, as discussed in the previous lesson (multiply the **F**irst terms, the** O**uter terms,** I**nside terms and the **L**ast terms).*

To expand three brackets, first expand two of the brackets, then use the result to expand with the final pair. Use a multiplication grid to help.

*Expand* $(x+1)(x+2)(x+3)$

*Answer*

*Take the first two brackets,* $(x+1)(x+2)$ *and multiply out using a grid.*

$\times$ | $\boldsymbol{x}$ | $\bold{+1}$ |

$\boldsymbol{x}$ | $x^2$ | $+x$ |

$\bold{+2}$ | $+2x$ | $+2$ |

*Add the terms and simplify*

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

*Substitute back into the original question*

$(x+1)(x+2)(x+3) = (x^2 + 3x+2)(x+3)$