Convert the Function f(x) = (2x + 1)(x - 2) into Standard Form

To find the standard representation of the function $f(x) = (2x + 1)(x - 2)$, we'll follow these steps to expand and simplify the expression:

• Step 1: Distribute each term of the first binomial over each term of the second binomial using the FOIL method.
• Step 2: Combine like terms to express the function in standard quadratic form.

Now, let's expand the expression:
1. Multiply the first terms: $2x \cdot x = 2x^2$
2. Multiply the outer terms: $2x \cdot (-2) = -4x$
3. Multiply the inner terms: $1 \cdot x = x$
4. Multiply the last terms: $1 \cdot (-2) = -2$

Next, we combine these results:
- The $2x^2$ term remains as is.
- Add the linear terms: $-4x + x = -3x$
- The constant term is $-2$.

Thus, the expanded and simplified form of the function is:
$f(x) = 2x^2 - 3x - 2$

The final expression in standard form is $f(x) = 2x^2 - 3x - 2$.