Question

I need help trying to work this problem out, 8a^3+27? the result comes out to be
(2a+3)(4a^2-6a+9). i just dont how you get that
answer.

Answer 1

Well you know that 8 and 27 are both cubes, (2, and 3 respectively) so you can start that way. Secondly you know that there aren't any middle terms, thus they must cancel in the cubing process. There is a formulaish way: \[(\beta a + \gamma)(\beta^2a^2 - (\beta\gamma) a + \gamma^2)\] if the cube is \[(\beta a^3 + \gamma^3)\] or
\[(\beta - \gamma)(\beta a^2 + (\beta\gamma)a + \gamma^2)\] if it is \[(\beta^3 - \gamma^3)\]

Answer 2

thank you. this formula and cubing is a little confusing at times. But I am trying to plug it in to help show the work to get the result. so this is taking some time.