how to factor 8x^3+27?
8x^3+27=0
8x^3=-27
x^3=-(27/8)
x=-3/2
proof
8(-3/2)^3=27=0
8(-27/8)+27=0
-27+27=0
0=0
To factor the expression 8x^3 + 27, we need to apply the formula for factoring the sum of cubes. The sum of cubes formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
In your expression, we have 8x^3 + 27. We need to identify 'a' and 'b' in order to apply the formula. Notice that 8x^3 can be written as (2x)^3, and 27 can be written as (3)^3.
Thus, we rewrite the expression as follows: (2x)^3 + (3)^3. Now we can apply the formula for sum of cubes:
(2x + 3)((2x)^2 - (2x)(3) + (3)^2)
Simplifying further, we get:
(2x + 3)(4x^2 - 6x + 9)
So, 8x^3 + 27 can be factored as (2x + 3)(4x^2 - 6x + 9).