how do you factor our a cube?
x^3 +8
memorize this pattern
A^3 + B^3 = (A+B)(A^2 - AB + B^2)
A^3 - B^3 = (A-B)(A^2 + AB + B^2)
x^3 +8
=> x^3 + 2^3
now apply the formula of a^3 + B^3
To factor a cube, we can make use of the formula for factoring the sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2). In your given expression, x^3 + 8, we can identify that 8 is a perfect cube which is equal to 2^3.
Now, we can rewrite the expression as (x)^3 + (2)^3. To factor it, we use the sum of cubes formula:
(x^3 + 8) = (x + 2)(x^2 - 2x + 4).
Thus, the factored form of x^3 + 8 is (x + 2)(x^2 - 2x + 4).