Factorize and simplify
8a⁶+ 729
First, we need to express 729 as a cube.
729 = 9^3
Therefore, the expression can be written as:
8a^6 + 9^3
Now, we can factorize by using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2):
8a^6 + 9^3 = (2a^2)^3 + (3)^3
= (2a^2 + 3)(4a^4 - 6a^2 + 9)
Therefore, the fully factorized and simplified expression is:
(2a^2 + 3)(4a^4 - 6a^2 + 9)