# Factor out COMPLETELY

Printable View

• August 30th 2010, 08:16 PM
chopstixdcb
Factor out COMPLETELY
Please provide steps to factoring out this expression:

x^3 y^2 - 9x^3 - 8y^2 + 72

Thanks much!
• August 30th 2010, 08:23 PM
mathaddict
Quote:

Originally Posted by chopstixdcb
Please provide steps to factoring out this expression:

x^3 y^2 - 9x^3 - 8y^2 + 72

Thanks much!

$x^3 (y^2-9)-8 (y^2-9)=0$

$(y^2-9)(x^3-8)=0$

Then here, make use of the identities:

$a^2-b^2=(a+b)(a-b)$

$
a^3-b^3=(a-b)(a^2+ab+b^2)$
• August 30th 2010, 08:30 PM
chopstixdcb
So is this right?

(x-2)(x^2+2X+4)(y+3)(y-3)(y+3)(y-3)?
• August 30th 2010, 08:36 PM
mathaddict
Quote:

Originally Posted by chopstixdcb
So is this right?

(x-2)(x^2+2X+4)(y+3)(y-3)(y+3)(y-3)?

Why did you give an extra of 2 factors? The last 2?
• August 30th 2010, 08:47 PM
chopstixdcb
I forgot, I understand now. The (y^2-9) allows me to group the (x^3-8). So I don't need those last two factors. Thanks so MUCH!