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

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

• A. \( x^2 - x - 6 \)
• B. \( x^2 - 5x - 6 \)
• C. \( x^2 - x + 6 \)
• D. \( x^2 + x - 6 \)

Answer: (A)

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

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