Factoring Cubes: 8x^3 - 125 = 8x^3 - 5^3 = (2x - 5)(4x^2....

chesterdg123 said:
To factor a difference of cubes: 8x^3-125
8x^3-5^3
(2x-5)(4x^2-40x+25)
Click to expand...
To check your factorization, multiply it back; if you get what you'd started with, you're probably fine.

In your case:

Code: 
        4x^2 -  40x +  25
                 2x -   5
-------------------------
       20x^2 - 200x - 125
8x^3 - 80x^2 +  50x
-------------------------
8x^3 - 60x^2 - 150x - 125
Hint: Check your signs against those in the "factoring differences of cubes" formula they gave you. :wink:

Eliz.
 
\(\displaystyle a^3-b^3 = (a-b)(a^2+ab+b^2)\)
\(\displaystyle a^3+a^3 = (a+b)(a^2-ab+b^2)\)

Memorize!!!
 
Thanks, I made a mistake the first time, but it appears that it is now correct. I just don't understand why it doesn't add (multiply) up like the other problems.
 
chesterdg123 said:
I just don't understand why it doesn't add (multiply) up like the other problems.
Click to expand...
On what basis do you feel that multiplication, in this particular instance, is not functioning in the usual way?

Please be complete. Thank you! :D

Eliz.
 
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