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.
#y^2-y-30#
#\begin{array}{rcl}
\left(y-6\right) \cdot \left(y + 5 \right) &=& y \cdot y + y \cdot 5 -6 \cdot y -6 \cdot 5 \\ &&\phantom{xxx}\blue{\text{rule \(\left(a+b\right) \cdot \left(c+d\right) = a \cdot c + a \cdot d + b \cdot c + b \cdot d\) }}\\
&=& y^2 + 5\cdot y -6\cdot y -30
\\&&\phantom{xxx}\blue{\text{multiplied }}\\
&=& y^2-y-30
\\&&\phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
#\begin{array}{rcl}
\left(y-6\right) \cdot \left(y + 5 \right) &=& y \cdot y + y \cdot 5 -6 \cdot y -6 \cdot 5 \\ &&\phantom{xxx}\blue{\text{rule \(\left(a+b\right) \cdot \left(c+d\right) = a \cdot c + a \cdot d + b \cdot c + b \cdot d\) }}\\
&=& y^2 + 5\cdot y -6\cdot y -30
\\&&\phantom{xxx}\blue{\text{multiplied }}\\
&=& y^2-y-30
\\&&\phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
Unlock full access
Teacher access
Request a demo account. We will help you get started with our digital learning environment.
Student access
Is your university not a partner?
Get access to our courses via Pass Your Math independent of your university. See pricing and more.
Or visit omptest.org if jou are taking an OMPT exam.
Or visit omptest.org if jou are taking an OMPT exam.