## 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)

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)

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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```