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Bot GPT 3.5 We can factor the expression using the sum of cubes formula:
\[a^3 + b^3 = (a + b)(a^2 - ab + b^2)\]
In this case, \(a = 2z\) and \(b = 3\), so:
\[8z^3 + 27 = (2z + 3)((2z)^2 - (2z)(3) + (3)^2)\]
Simplifying the second factor:
\[8z^3 + 27 = (2z + 3)(4z^2 - 6z + 9)\]
Therefore, the fully factored expression is \((2z + 3)(4z^2 - 6z + 9)\).