okay, so how do you factor 64x^3-8?

Question

anonymous · Answer

64=4^3
8=2^3
use$$x^3-y^3=(x-y)(x^2+xy+y^2)$$

anonymous · Answer

that doesn't exactly help me..

saifoo.khan · Answer

There's a formula for solving problems like these.
@jonask wrote that formula above.

anonymous · Answer

So for example 
$$1000x^3 - 125y^3\to (10x)^3-(5y)^3$$
Using SOAP
$$(10x-5y)((10x)^2+(10x)(5y)+(5y)^2)$$
and then you clean up thingsl like 10x5y=50xy and stuff like that

anonymous · Answer

okay, the answer is 8(2x-1)(4x^2+2x+1). I'm not sure how to get that...

anonymous · Answer

Were you able to apply the SOAP method to your problem? 
could you convert $$64x^3\rightarrow ()^3$$
?

anonymous · Answer

yea, I got 64x^3-8=(4x)^3-2^3=(4x-2)(16x^2+8x+4). I don't know what to do from there

anonymous · Answer

factor factor factor. 
1) what # can you factor from (4x-2) ? 
2) what # can you factor from (16x^2+8x+4)?

anonymous · Answer

BTW, you did the SOAP correctly:)

anonymous · Answer

err....I'm not totally sure...

anonymous · Answer

I'll do the first one and you can do the second. 

(4x+2) = 2(2x+1)
since you can divide 4 and 2 by 2:)

anonymous · Answer

What is the larges integer number that divides 16, 8, and 4?

anonymous · Answer

4, and then you multiply two and 4 and that's where the 8 comes from! I see!

anonymous · Answer

Yay! Remember, next to perseverence (sp?), Factoring is probably the most important skill for math

anonymous · Answer

thank you!

anonymous · Answer

use polynomial division procedure:D