Algebra: Expanding brackets
Expanding brackets
We often see brackets in mathematical expressions. It is, therefore, useful to know how to expand those brackets.
Example \[\begin{array}{rcl}\blue2 (\green{x}+\purple{2})&=&\blue{2} \green{x} + \blue{2}\cdot \purple{2} |
Example \[\begin{array}{rcl}(\blue{2}+\green{y}) \purple{x}&=& \blue{2} \purple{x} + \green{y} \purple{x} \\ |
#-3\cdot a + 9#
#\begin{array}{rcl}
-3 \cdot \left(a-3\right)&=& -3 \cdot a -3 \cdot -3
\\ &&\phantom{xxx}\blue{\text{rule \(a \cdot \left(b+c\right) = a \cdot b + a \cdot c\) }}\\
&=& -3\cdot a + 9
\\ &&\phantom{xxx}\blue{\text{multiplied }}\\
\end{array}#
#\begin{array}{rcl}
-3 \cdot \left(a-3\right)&=& -3 \cdot a -3 \cdot -3
\\ &&\phantom{xxx}\blue{\text{rule \(a \cdot \left(b+c\right) = a \cdot b + a \cdot c\) }}\\
&=& -3\cdot a + 9
\\ &&\phantom{xxx}\blue{\text{multiplied }}\\
\end{array}#
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