which is a factored form of 27x^3+64?
answer is (3x + 4)(9x^2 - 12x + 16)
work out
To find the factored form of the expression 27x^3 + 64, we need to determine its factors.
Let's start by recognizing that this is a sum of cubes, which can be expressed as (a^3 + b^3) = (a + b)(a^2 - ab + b^2).
In our expression, 27x^3 + 64, the first term can be written as (3x)^3 and the second term as 4^3.
Using the sum of cubes formula, we have:
(3x)^3 + 4^3 = (3x + 4)((3x)^2 - (3x)(4) + 4^2)
= (3x + 4)(9x^2 - 12x + 16).
Therefore, the factored form of 27x^3 + 64 is (3x + 4)(9x^2 - 12x + 16).