use the difference of squares to factor the expression
36x^8-9y^4

Question

use the difference of squares to factor the expression 
36x^8-9y^4

anonymous · Answer

36

turingtest · Answer

yeah, that's nonsense above

anonymous · Answer

Hi Turing! I understand factoring to a point, but not this specific method, would you be willing to walk me through it? :)

anonymous · Answer

wait, this should be in the math section right?

anonymous · Answer

oh I actually thought I put it in the math section!
Completely my bad!

turingtest · Answer

lol I just followed the link, I didn't even know where we were :P

turingtest · Answer

difference of squares is the formula$$a^2-b^2=(a-b)(a+b)$$so you need to identify:
what is a and b in you problem
compare and contrast:
the form$$a^2-b^2=(a+b)(a-b)$$and yours$$36x^8-9y^4$$what are $a$ and $b$ in your particular case?

anonymous · Answer

Sorry guys! I was talking in math chat and didn't pay attention to the actual page I was on!

turingtest · Answer

honest mistake, no worries :)

anonymous · Answer

a =36 and b= 9 ?

turingtest · Answer

good effort, but notice a few things...

turingtest · Answer

we need to keep the variables, so don't just drop x and y
also not that I asked you what $a$ and $b$ are, but the formula starts with $a^2$ and $b^2$
so in your case, $a^2=36x^8$
so what is $b^2$ ?

turingtest · Answer

also note*

anonymous · Answer

b^2 = 9y^4 ?

turingtest · Answer

yes :)
so if 
a^2=36x^8
and
b^2=9y^4

then what are a and b ?

anonymous · Answer

I dont know :( would this be where I start factoring?

anonymous · Answer

would I take the square root of 36x^8?  im so bad at this. but im thinking haha.

turingtest · Answer

yes, you just take the square root
if$$a^2=36x^8$$then $$a=\sqrt{36x^8}$$

turingtest · Answer

simplify...

anonymous · Answer

6 sq root(x^8) sorry I dont know how to make the square root symbol

turingtest · Answer

that's fine, but what is $$\sqrt{x^8}$$ ???
you can simplify that

anonymous · Answer

x^4?

anonymous · Answer

6x^4 so then b = 3y^2?

turingtest · Answer

you got it :)
now just plug those values of a and b into the formula for difference of squares I wrote above

anonymous · Answer

36x^8 - 9y^4 = (6x^4 -3y^2) (6x^4 +3y^2) ? :)

turingtest · Answer

yep :) good job!
think you got the idea ?

anonymous · Answer

yes! thanks so much! im actually super excited that I get it now!

turingtest · Answer

that's all I can hope for :)

turingtest · Answer

welcome!