Thread: polynomial

1. polynomial

help with another one please, Express as a polynomial.
(x+a){x^2-ax/x}, my answer is x^2-2ax+a^2, but not sure if it could be x^2-2ax-a^2, thanks for checking.

2. Originally Posted by wayne
help with another one please, Express as a polynomial.
(x+a){x^2-ax/x}, my answer is x^2-2ax+a^2, but not sure if it could be x^2-2ax-a^2, thanks for checking.
If you've been doing factoring you should know how to multiply these out. (I mean, without relying on FOIL, but it depends on how you're being taught.)

$(x + a) \left ( \frac{x^2 - ax}{x} \right )$

$= \frac{(x + a)(x^2 - ax)}{x}$

$= \frac{x(x^2 - ax) + a(x^2 - ax)}{x}$

$= \frac{(x^3 - ax^2) + (ax^2 - a^2x)}{x}$

$= \frac{x^3 - a^2x}{x}$

$= \frac{x(x^2 - a^2)}{x}$

$= x^2 - a^2$

-Dan

Edit: Or I suppose you could've simply done
$\frac{x^2 - ax}{x} = x - a$
immediately and multiplied out from there.

3. I should have,

so I should have x^2-a^2, thanks for looking this over.

4. Originally Posted by wayne
so I should have x^2-a^2, thanks for looking this over.
No prob!

-Dan