### Algebra: Expanding brackets

### Expanding brackets

We will often see brackets in mathematical expressions. It is very useful to know how to expand those brackets.

\[\begin{array}{rcl}\blue2 (\green{x}+\purple{2})&=&\blue{2} \green{x} + \blue{2}\cdot \purple{2} |

\[\begin{array}{rcl}(\blue{2}+\green{y}) \purple{x}&=& \blue{2} \purple{x} + \green{y} \purple{x} \\ |

#-7\cdot a -42#

#\begin{array}{rcl}

-7 \cdot \left(a+6\right)&=& -7 \cdot a -7 \cdot 6

\\ &&\phantom{xxx}\blue{\text{rule \(a \cdot \left(b+c\right) = a \cdot b + a \cdot c\) }}\\

&=& -7\cdot a -42

\\ &&\phantom{xxx}\blue{\text{multiplied }}\\

\end{array}#

#\begin{array}{rcl}

-7 \cdot \left(a+6\right)&=& -7 \cdot a -7 \cdot 6

\\ &&\phantom{xxx}\blue{\text{rule \(a \cdot \left(b+c\right) = a \cdot b + a \cdot c\) }}\\

&=& -7\cdot a -42

\\ &&\phantom{xxx}\blue{\text{multiplied }}\\

\end{array}#

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