Question

How do you simplify the product `(a^2 + a + 1)(a - 1)` and write it in standard form?

Answer 1

`a^3-1`

Explanation:

multiplying a polynomial by a binomial has the same steps as multiplying two binomials. take the first variable and multiply it by the variables, in order, in the second brackets.

`(a^2+a+1)(a-1)`

first multiply `a^2` by `a` and then by `1`. follow suit with the `a` and the `+1`

`a^3 - a^2 + a^2 - a + a - 1`

collect like terms. the `a^2` and the `a` will cancel each other out.

`a^3 - 1`