# Math Help - Factoring with exponents

1. ## Factoring with exponents

Please help me factor the following:

81y^4-w^4y^4

Thanks in advance for your help.

2. $81y^4-w^4y^4$

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

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

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

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

3. Stroodle, many thanks for your quick response and help!

4. 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?

Thank you in advance for your help.

5. Anyone else is welcome to jump in to and explain as well.

Thanks in advance.

6. $(81-w^4)$

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
$

7. 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.