FOIL
We use this method when we have to expand two sets of brackets, each having two variables or constants, let’s take a look at an example to see what this means:
Each set of brackets has two expressions, the first set of brackets has “+2x” and “-9” and the second set of brackets has “+3x”and “+3”, so in total we have for elements to be multiplied together in some way to fully expand this expression. The way that we do this is called FOIL and this stands for “First, Outer, Inner, Last”:
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FIRST |
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OUTER |
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INNER |
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LAST |
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You can see that using this method makes sure that each element in the first set of brackets is multiplied by each one in the second, so overall you have performed four multiplications. This method can be amended to cater for brackets containing more expressions but for the moment we will stick with brackets containing two each.
Let’s take a look the result of our efforts:
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FIRST |
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OUTER |
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INNER |
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LAST |
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We now have to collect all of our “like” terms and come up with a final result for our expansion. In this case we have to combine “+6x” and “-27x” making “-21x”, our final expression then becomes:
We can of course work backwards, from this “quadratic expression” and end up with the two sets of brackets that we started with. This would be more complicated and is something that we will come to later.
Remember:
- Brackets placed side by side means that they are multiplied.
- If you can’t see a sign, it’s a “+” (e.g. +6x2)
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