SOLUTION: Hi, I have forgotten the formula and reason for factorising eg. x^3 -8. Could someone please explain it to me again? Thanks!

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Question 1017814: Hi, I have forgotten the formula and reason for factorising eg. x^3 -8.
Could someone please explain it to me again? Thanks!
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try using polynomial division if you do not have the formula already memorized for Difference of Cubes.

You want some factor being cubed OR two factors to give you 8. 
             x^2      2x         4

      ----------------------------------------------------
x-2   |      x^3      0*x^2       0*x      -8
      |      x^3      -2x^2
             ---------------
              0      2x^2        0*x
                     2x^2        -4x
                    -----------------
                       0        4x         -8
                                4x         -8
                               ----------------
                                 0         0

x%5E3-8=highlight%28%28x-2%29%28x%5E2%2B2x%2B4%29%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The general formula is

a%5E3+-+b%5E3 = %28a-b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29.

See the lesson The difference of cubes formula in this site.

It is like 2 x 2 = 4. Of the same fundamental level.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, I have forgotten the formula and reason for factorising eg. x^3 -8.
Could someone please explain it to me again? Thanks!
x%5E3+-+8

%28x%29%5E3+-+%282%29%5E3

(x  2)(x2  2x  22)

(x  2)(x2  2x   4)

highlight_green%28%28x+-+2%29%28x%5E2+%2B+2x+%2B+4%29%29 ------- Applying Mnemonic, SDP