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

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

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

Postby bird on 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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  TOPIC_SOLVED

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

bird wrote: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.

bird wrote:(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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