Question

Multiply Linear Expressions Quick Check
4 of 54 of 5 Items
Question
Multiply (x+3)(x−2)
.(1 point)
Responses

x2+x−6
x squared plus x minus 6

x2+5x+6
x squared plus 5 x plus 6

x2−6
x squared minus 6

x2−5x+6

Answer 1

To multiply the linear expressions \((x+3)(x-2)\), you can use the distributive property (also known as the FOIL method for binomials):

1. First, multiply the first terms: \(x \cdot x = x^2\)
2. Then, multiply the outer terms: \(x \cdot -2 = -2x\)
3. Next, multiply the inner terms: \(3 \cdot x = 3x\)
4. Finally, multiply the last terms: \(3 \cdot -2 = -6\)

Now add all these together:

\[
x^2 - 2x + 3x - 6 = x^2 + (3x - 2x) - 6 = x^2 + x - 6
\]

So, the result of multiplying \((x+3)(x-2)\) is:

\[
\boxed{x^2 + x - 6}
\]

The correct response is: **x^2 + x - 6**.