Factor

Question

8z^3+27

Answer 1

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 \((2z + 3)(4z^2 - 6z + 9)\).