Help me factor..its so hard for me please teach me how?!?

Question

I need to factor these polymonial
x^3+64
what are the rules of it? please help me i want to learn to factor
also how do u factor 125x^3-8

Answer 1

sum of two cubes, you could write it as
x^3+4^3
formula
X 3+ Y 3 = (x + y)(X 2 - XY + Y 2 )
(x+4)(x^2-4x+16)

Answer 2

First, you can tell that both x^3 and 64 are cubes, x^3 is x cubed and 64 is 4 cubed. Since these cubes are being added together it can be classified as a sum of cubes problem. The equation for a sum of cubes is:
(a+b)(a^2-ab+b^2)=a^3+b^3
a=x and b=4 then just plug it in:
(x+4)(x^2-4x+16) and whenever it is a sum or difference of cubes you can't factor it any farther.

The second one is the same principle except it is a difference of cubes because of the minus sign. The equation for a difference of cubes is:
(a-b)(a^2+ab+b^2)
For this problem it a=5x and b=2 so the answer is:
(5x-2)(25x^2+10x+4)
I hope I explained it well enough to help.

Answer 3

(a+b) (a^2 - ab + b^2 ) = a^3 + b^3
(a-b)(a^2+ab+b^2) = a^3 - b^3
(similar results apply for higher powers)

x^3+64 = x^3 + 4^3 = (x+4)( x^2 -4x+16)
125x^3-8 = (5x)^3 - 2^3 = (5x-2)(25x^2+10x+4)

Answer 4

sum of two cubes
x^3+64
(A^3 + B^3)=(A+B)(A^2 - AB + B^2)
(x^3 + 4^3) =(x+4) (x^2-4x+4^2)
(x^3 + 4^3) (x+4)(x^2 -4x+ 16)
difference of two cubes
125x^3-8
(a^3-b^3)=(a-b)(a^2+ab+b^2)
(5x^3-2^3)=(5x-2)(5x^2+(5x)(2)+2^2)
(5x^3-2^3)=(5x-2)(25x+10x+4)