This is pretty much the same as single brackets, except more complex. For example:
Expand and simplify (x + 2)(x - 3).
So, we multiply EVERTHING OUTSIDE THE BRACKET (i.e. the whole first bracket) by EVERTHING INSIDE THE BRACKET (i.e. the whole second bracket).
We can do this by one of two ways:
1. Using FOIL. This stands for First, Outside, Inside, Last. First, we multiply the first terms in each bracket: x and x. This makes x2.
Outside - multiply the terms on the outside of the expression (the first term of the first bracket and the last term of the second). This is x and -3, which comes to -3x.
Inside - now multiply the terms on the INSIDE of the expression: 2 and x, which is 2x.
The Last terms in each bracket are 2 and -3, which multiply to make -6.
We now add all these together:
x2 - 3x + 2x - 6
This simplifies to:
x2 - x - 6
We can also plot a table:
times x -3
x x2 -6
+2 +2x -6
And, if we add these and simplify, this gives us the exact same answer!
Peronally, I prefer to use a table, but FOIL works just as well. Here is our quick quiz to test yourself with:
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