8x^3 + 27 factor the sum or difference of two cubes. Please show work.
You must know that
A^3 + B^3 = (A+B)(A^2 - AB + b^2)
so 8x^3 + 27)
= (2x + 3)(4x^2 - 6x + 9)
To factor the given expression, 8x^3 + 27, we can use the formula for factoring the sum of two cubes, which states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
In this case, we have 8x^3 + 27, which can be viewed as (2x)^3 + 3^3. Now, we can see that a = 2x and b = 3. Using the formula mentioned above, we can write the expression as:
(2x + 3)((2x)^2 - (2x)(3) + (3)^2)
= (2x + 3)(4x^2 - 6x + 9)
Therefore, the factored form of 8x^3 + 27 is (2x + 3)(4x^2 - 6x + 9).