Algebra: Expanding brackets
Expanding double brackets
We have seen how we can expand single brackets. We can also expand double brackets. We can do so using the banana method.
The banana method
Example |
In the same way, we can also work with more complicated products.
#b^2+10\cdot b+25#
#\begin{array}{rcl}
\left(b+5\right) \cdot \left(b + 5 \right) &=& b \cdot b + b \cdot 5 + 5 \cdot b + 5 \cdot 5 \\ &&\phantom{xxx}\blue{\text{rule \(\left(a+b\right) \cdot \left(c+d\right) = a \cdot c + a \cdot d + b \cdot c + b \cdot d\) }}\\
&=& b^2 + 5\cdot b + 5\cdot b + 25
\\&&\phantom{xxx}\blue{\text{multiplied }}\\
&=& b^2+10\cdot b+25
\\&&\phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
#\begin{array}{rcl}
\left(b+5\right) \cdot \left(b + 5 \right) &=& b \cdot b + b \cdot 5 + 5 \cdot b + 5 \cdot 5 \\ &&\phantom{xxx}\blue{\text{rule \(\left(a+b\right) \cdot \left(c+d\right) = a \cdot c + a \cdot d + b \cdot c + b \cdot d\) }}\\
&=& b^2 + 5\cdot b + 5\cdot b + 25
\\&&\phantom{xxx}\blue{\text{multiplied }}\\
&=& b^2+10\cdot b+25
\\&&\phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
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