Expand and simplify quadratics
A pair of brackets can be expanded to give a quadratic expression.
It’s important to remember that when dealing with algebra problems both terms in the first bracket must be multiplied by both terms in the second bracket. You should always finish with four terms, e.g.
(x + 2)(x + 3) = x2 + 3x + 2x + 6
Since there are two x terms, the last step is to simplify by collecting the like terms:
x2 + 3x + 2x + 6 = x2 + 5x + 6
A very common error is to multiply only the x from the brackets together, and then the multiply only the numbers together.
This is WRONG! - (x + 2)(x + 3) = x2 + 6
As you can see, this would lose the x terms in the middle.
Now let's try on more example to make sure we have got this down!
(x + 7)(x + 2) = x2 + 2x + 7x + 14
Now we can simplify by collecting the like terms:
x2 + 2x + 7x + 14 = x2 + 9x + 14
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