Question

Factor the polynomial completely.
\[a^4 - b^4\]

Answer 1

hi!!

Answer 2

do you know how to factor the difference of two squares?

Answer 3

Hello! :)

Answer 4

I think....

Answer 5

try, i will tell you if you are right

Answer 6

Well, I am not sure what the first step is... >_<

Answer 7

Especially with a problem like this.... :(

Answer 8

hint:
\[a^4-b^4=(a^2)^2-(b^2)^2\]

Answer 9

now see if that reminds you of something you know

Answer 10

okay let's you do this :)

Answer 11

So it would be: \((a^2)^2 - (b^2)^2\)

Answer 12

What is the next step? :)

Answer 13

what is \[a^2-b^2=?\]

Answer 14

Do you recall the difference of two squares?

Answer 15

Ummmm....

Answer 16

No...?

Answer 17

hmm eh, how are you supposed to factor without that then lol

Answer 18

okay so we have \[(a-b)(a+b)=a^2-b^2\]

Answer 19

if you expand you will get the right hand side

Answer 20

so \[(a^2)-(b^2)^2=(a^2-b^2)(a^2+b^2)\]

Answer 21

Oh! I was supposed to say that (a - b)(a + b) when you asked earlier...

Answer 22

of course not, that's just a refresher to you
since you don't remember that

Answer 23

Oh... Okay.

Answer 24

yes of course, blah, you made me worthless talking for minutes for nothing

Answer 25

ok then take what i did and go further then

Answer 26

So, you are saying that \((a^2)^2 - (b^2)^2\) can be simplified further?

Answer 27

To something like \((a^2-b^2)(a^2+b^2)?\)

Answer 28

@xapproachesinfinity ^

Answer 29

(a-b)(a+b)(a^2+b^2) should be this

Answer 30

gotta leave

Answer 31

Wait, that's the final answer? \[(a-b)(a+b)(a^2+b^2)\]

Answer 32

\[\Huge ???\]

Answer 33

\[\Huge \ddot \frown\]