Which expression represents \( (x - 3)(x + 2) \) when expanded?

To expand the expression ( (x - 3)(x + 2) ), we use the distributive property, commonly referred to as the FOIL method for binomials. This stands for First, Outside, Inside, and Last, representing the terms we will multiply.

1. First: Multiply the first terms in each binomial, which are ( x ) and ( x ). This gives ( x^2 ).

2. Outside: Multiply the outer terms, which are ( x ) and ( 2 ). This results in ( 2x ).

3. Inside: Multiply the inner terms, which are ( -3 ) and ( x ). This produces ( -3x ).

4. Last: Multiply the last terms in each binomial, which are ( -3 ) and ( 2 ). This results in ( -6 ).

Putting these results together, we have:

[

x^2 + 2x - 3x - 6

]

Now, combine the like terms ( 2x - 3x ) to simplify:

[

x^2 - x - 6

]

Thus