How do you solve the equation 81t3 - 81t equals 0?

Answer 1

You factor it.

81t3 - 81t = 0

Divide by 81:

t3 - t = 0

Take out the common factor t:

t (t2 - 1) = 0

Here we have a difference of two squares, therefore:

t (t + 1) ( t - 1) = 0

If the product is zero, that means that one of the factors must be zero, so you have to solve the three equations:

t = 0 OR t + 1 = 0 OR t - 1 = 0.

In summary, t can be 0, -1, or 1.