Cube a binomial by writing it three times and multiplying each term by using an extrapolated FOIL method. In other words, multiply first terms, outside terms, inside terms, and last terms before combining like terms to achieve the final result.
- Write the problem
The binomial should be expressed in parentheses to denote multiplication.
- Multiply the first two binomials to produce a trinomial
For an example problem, cube the binomial (x - 3). Write it as (x - 3)(x - 3)(x - 3). Multiply the first x by x, then by -3. Then, multiply -3 by x and by -3. Combine like terms. This yields the term (x^2 - 6x + 9).
- Multiply the trinomial by the binomial.
The example now should appear as (x^2 - 6x + 9)(x - 3). For convenience, it can be rewritten the other way around. Now, multiply the first term by each of the other terms in the other expression in sequence: x^2 should be multiplied by x, then by -3; -6x multiplied by x and then by -3 and so on. The final result is x^3 - 3x^2 - 6x^2 + 18x + 9x - 27. Simplified, this yields x^3 - 9x^2 + 27x - 27.