# Factoring with exponents

• Dec 16th 2009, 07:18 AM
dkpeppard
Factoring with exponents

81y^4-w^4y^4

• Dec 16th 2009, 07:37 AM
Stroodle
$81y^4-w^4y^4$

$y^4(81-w^4)$

$y^4(9+w^2)(9-w^2)$

$y^4(9+w^2)(3+w)(3-w)$

$-y^4(w^2+9)(w+3)(w-3)$
• Dec 16th 2009, 07:38 AM
dkpeppard
Stroodle, many thanks for your quick response and help!
• Dec 17th 2009, 06:30 AM
dkpeppard
Quote:

Originally Posted by Stroodle
$81y^4-w^4y^4$

$y^4(81-w^4)$

$y^4(9+w^2)(9-w^2)$

$y^4(9+w^2)(3+w)(3-w)$

$-y^4(w^2+9)(w+3)(w-3)$

Stroodle,

In trying to understand how this is factored, how did you get to the second step, please?

$y^4(81-w^4)$

Could you break that down and explain it a little further for me, please?

• Dec 17th 2009, 09:45 AM
dkpeppard
Anyone else is welcome to jump in to and explain as well.

• Dec 17th 2009, 10:49 AM
bigwave
$(81-w^4)$

this is a difference of squares

$
(9-w^2)(9+w^2)
$

if you FOIL this the middle terms will cancel out

$
81 + w^2 -w^2-w^4
$

leaving

$
81-w^4
$
• Dec 17th 2009, 10:53 AM
dkpeppard
Quote:

Originally Posted by bigwave
$(81-w^4)$

this is a difference of squares

$
(9-w^2)(9+w^2)
$

if you FOIL this the middle terms will cancel out

$
81 + w^2 -w^2-w^4
$

leaving

$
81-w^4
$

Thank you, Bigwave.