How do you solve #(t+1)^3=t^3+7#?
Splitting middle term
The two solutions are
Expand the cube, using the formula
In words, the cube of a sum is given by the sum of the two cubes, and the triple product of the square of an element and the other. In our case:
Writing the whole equation, we see that the cubes cancel out:
Thus, the two solutions are