cubed equation: 2t^3 - 54 = 2(t^3 - 27) = ??

[Failenn]

Have problem 2t^3 -54. I know I start by taking out the 2 and that gives me

2(t^3-27) which is a perfect cube. What i'm having troubles remembering is the rule and so I came up with two different answers. the first one i think is correct.

2(t-3)(t^2 + 6t + 9)

2(t-3)(t^2 +3t + 9)

 

[Deleted member 4993]

Re: cubed equation

Have problem 2t^3 -54. I know I start by taking out the 2 and that gives me

2(t^3-27) which is a perfect cube. What i'm having troubles remembering is the rule and so I came up with two different answers. the first one i think is correct.

2(t-3)(t^2 + 6t + 9)

2(t-3)(t^2 +3t + 9)<<< Correct one - multiply it out to check.

\(\displaystyle a^3 \, - \, b^3 \, = \, (a \, - \, b)\cdot (a^2 \, + \, ab \, + \, b^2)\)

 

[Failenn]

Thank you. I had not thought to remuliply it out. I wrote the "formula" down in a mini spiral notebook. I've taken to doing that so I can review and know for tests and also as a reference I can use anytime.