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
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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 + 1178x^3 - 56x^2 + 72x`