What are the instructions for cubing a binomial? The problem is (x-1)^3
To cube a binomial, such as (x-1)^3, you can follow these steps:
1. Start by writing the binomial three times in a row: (x-1)(x-1)(x-1).
2. Multiply the binomials together using the distributive property. Multiply the first terms, the outer terms, the inner terms, and finally the last terms.
(x-1)(x-1)(x-1) = (x * x * x) + (x * x * -1) + (-1 * x * x) + (-1 * -1 * x) + (-1 * -1 * -1)
3. Simplify each term by multiplying the variables and constants together:
(x * x * x) = x^3
(x * x * -1) = -x^2
(-1 * x * x) = -x^2
(-1 * -1 * x) = x
(-1 * -1 * -1) = -1
4. Combine the simplified terms:
x^3 + (-x^2) + (-x^2) + x + (-1) = x^3 - 2x^2 + x - 1
So, the cube of the binomial (x-1) is x^3 - 2x^2 + x - 1.