Factor the following expression completely: 36^3-16x
(36)^3 - 16X =
46656 - 16X =
16(2916 - X).
To factor the expression 36^3 - 16x completely, we need to apply the difference of cubes formula. The difference of cubes formula states that for any two numbers a and b, we can factor the expression a^3 - b^3 as (a - b)(a^2 + ab + b^2).
In this case, a = 36 and b = 2x. Plugging these values into the formula, we have:
36^3 - 16x = (36 - 2x)(36^2 + (36)(2x) + (2x)^2)
Simplifying further, we have:
= (36 - 2x)(1296 + 72x + 4x^2)
Therefore, the expression 36^3 - 16x can be factored completely as (36 - 2x)(1296 + 72x + 4x^2).