Expand: (x^2-6x+9)(x^2+8x+13)

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
bird
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Expand: (x^2-6x+9)(x^2+8x+13)

Postby bird » Wed Mar 04, 2009 1:07 am

How should I start expanding two quadratics? Do I factor and then do it the long way?

(x^2-6x+9)(x^2+8x+13)

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stapel_eliz
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Postby stapel_eliz » Wed Mar 04, 2009 2:54 am

How should I start expanding two quadratics? Do I factor and then do it the long way?
Factoring is going in the wrong direction. You're not wanting to take this apart; you're wanting to multiply it all together.
(x^2-6x+9)(x^2+8x+13)
Once you have this many terms, vertical multiplication is probably the way to go. It's just so much simpler, usually...

So, just like you use vertical multiplication for multiplying three-digit and larger numbers, use a vertical set-up here:
start like this:

     x^2 - 6x +  9
     x^2 + 8x + 13
------------------
Then you'll multiply, starting with the right-most term of the lower row, just like in regular (numerical) multiplication:
first multiplication:

     x^2 -  6x +   9
     x^2 +  8x +  13
--------------------
   13x^2 - 78x + 117
Then you continue:
second multiplication:

         x^2 -  6x +   9
         x^2 +  8x +  13
------------------------
       13x^2 - 78x + 117
8x^3 - 56x^2 + 72x
Then do the third multiplication, and add down to get your answer. :D


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