81s^6-3f^6
Factor

- anonymous

81s^6-3f^6
Factor

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- amistre64

factor out the 3 and look for diff of squares

- amistre64

or even diff of cubes

- amistre64

27 is a cube so...

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## More answers

- amistre64

3(27s^6 - f^6)
3 (3s^2 -f^2) (9s^4 +3(sf)^2 +f^4) if I remember correctly; and then theres that diff of squares that it generated....

- amistre64

you have any with sqrt(3) in it?

- amistre64

3 (sqrt(3)s +f)(sqrt(3)s -f) (9s^4 +3(sf)^2 +f^4) but let me check thru that again

- anonymous

not they all have ^6

- amistre64

all the answers?

- smurfy14

3(3s^2-f^2)(9s^4+3f^2s^2+f^4)

- amistre64

3(27s^6 -f^6) is what it initially factor to

- amistre64

but thats a difference of cubes

- anonymous

ok so what shall I put in for the answer then please

- smurfy14

\[3(3s^2-f^2)(9s^4+3f^2s^2+f^4)\] is the answer

- amistre64

if we factor this completely i get:
3 .... yeah, like that again

- amistre64

but, that (3s^2 -f^2) factors again

- anonymous

so do u amistre64 agree with smurfy answer

- amistre64

\[3(\sqrt{3}+f)(\sqrt(3)-f)(9s^4 +3s^2 f^2 +f^2)\]

- anonymous

3(3s2−f2)(9s4+3f2s2+f4)

- amistre64

that (3) is a typo; just sqrt(3) like the other one lol

- anonymous

This is the answer: 3(3√+f)((√3)−f)(9s4+3s2f2+f2)

- amistre64

i just dont know what your material is looking for for an acceptable answer with that

- amistre64

\(\sqrt{3}\) is a valid number as far as i can tell

- anonymous

it just say factor sir

- anonymous

I think i'll learn partial differential equations before she learns how to factor

- amistre64

my gut says to go all the way ;)
\(3(\sqrt{3}+s)(\sqrt{3}-s)(9s^4+3s^2 f^2+f^4)\)

- anonymous

ok i will try it

- amistre64

ack..cant type lol

- anonymous

lordamercy. isn't this just the difference of two cubes?

- amistre64

make it:
\(3(\sqrt{3}s-f)(\sqrt{3}s+f)(9s^4 +3s^2 f^2 +f^4)\)

- amistre64

thats my final offer lol

- amistre64

its a diff of cubes with a diff of squares snucked in

- smurfy14

im telling you mine is correct you can check it if you dont believe me

- anonymous

3(3√+f)((√3)−f)(9s4+3s2f2+f2)

- amistre64

checking a partial simplification doesnt prove nuthin lol

- anonymous

amistre64 is smarter!

- amistre64

at times.... other times im just an idiot in disguise ;)

- anonymous

haha

- anonymous

ok smurfy you were right sorry

- smurfy14

thank you :)

- amistre64

yay!! smurfy

- amistre64

even tho i typed it in like that first ...... lol

- anonymous

\[3(27s^6-f^6)=3((s^2)^3-(f^2)^3\]\]
\[a^3-b^3=(a-b)(a^2+ab+b^2)\]
so you get \[3((3s^2)-f^2)((3s^2)^2+3s^2f^2+(f^2)^2)\]
\[3(3s^2-f^2)(9s^4+3s^2f^2+f^4)\]

- anonymous

hello amistre!

- amistre64

yes; and the question I had was do we take the diff of squares further?

- amistre64

howdy! :)

- anonymous

ahh i see . first term is difference of two squares, if you are factoring over reals. yes.

- amistre64

thats what I thought .....

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