### Reformatting the intake :

Changes made to your input should not affect the solution: (1): "x3" was changed by "x^3".

You are watching: X^3+8 factored completely

## Step 1 :

Trying to aspect as a distinction of Cubes:

1.1 Factoring: x3-8 concept : A difference of two perfect cubes, a3-b3 deserve to be factored into(a-b)•(a2+ab+b2)Proof:(a-b)•(a2+ab+b2)=a3+a2b+ab2-ba2-b2a-b3 =a3+(a2b-ba2)+(ab2-b2a)-b3=a3+0+0+b3=a3+b3Check:8is the cube that 2Check: x3 is the cube of x1Factorization is :(x - 2)•(x2 + 2x + 4)

Trying to aspect by splitting the center term

1.2Factoring x2 + 2x + 4 The an initial term is, x2 the coefficient is 1.The middle term is, +2x that is coefficient is 2.The critical term, "the constant", is +4Step-1 : multiply the coefficient the the very first term through the constant 1•4=4Step-2 : discover two components of 4 who sum equates to the coefficient the the middle term, i beg your pardon is 2.

 -4 + -1 = -5 -2 + -2 = -4 -1 + -4 = -5 1 + 4 = 5 2 + 2 = 4 4 + 1 = 5

Observation : No two such components can be uncovered !! Conclusion : Trinomial have the right to not it is in factored

## Final result :

(x - 2) • (x2 + 2x + 4)

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