Use the FOIL method to multiply the following binomials: (x+2)(x−1)

To use the FOIL method to multiply the binomials \((x + 2)(x - 1)\), we follow these steps:

1. **First**: Multiply the first terms of each binomial.
\[
x \cdot x = x^2
\]

2. **Outer**: Multiply the outer terms of the binomials.
\[
x \cdot (-1) = -x
\]

3. **Inner**: Multiply the inner terms of the binomials.
\[
2 \cdot x = 2x
\]

4. **Last**: Multiply the last terms of each binomial.
\[
2 \cdot (-1) = -2
\]

Now, combine all these results:
\[
x^2 - x + 2x - 2
\]

Next, combine the like terms \(-x\) and \(2x\):
\[
x^2 + x - 2
\]

So, the product of \((x + 2)(x - 1)\) is:
\[
\boxed{x^2 + x - 2}
\]