Question

Alex has a workshop with an area that can be modeled by the expression 4x2+7x−3
square feet. He agrees to rent out part of his workshop to his friend Matt. Alex agrees to let Matt use a space in his workshop that is 2x2+7x−5
square feet.

What is the expression that models the remainder of Alex's workshop space once he rents Matt his portion?

(1 point)
Responses

2x2−14x−8
square feet
2 x squared minus 14 x minus 8 square feet

6x2+14x−8
square feet
6 x squared plus 14 x minus 8 square feet

2x2−8
square feet
2 x squared minus 8 square feet

2x2+2
square feet
2 x squared plus 2 square feet

Answer 1

To find the expression that models the remainder of Alex's workshop space after renting out part to Matt, we need to subtract the area Matt is using from the total area of Alex's workshop.

The total area of Alex's workshop is given by the expression:
\[ 4x^2 + 7x - 3 \]

The area that Matt is renting is given by the expression:
\[ 2x^2 + 7x - 5 \]

Now we will perform the subtraction:

\[
(4x^2 + 7x - 3) - (2x^2 + 7x - 5)
\]

First, we distribute the negative sign across Matt's area:

\[
4x^2 + 7x - 3 - 2x^2 - 7x + 5
\]

Now, we can combine like terms:

1. The \(x^2\) terms:
\[ 4x^2 - 2x^2 = 2x^2 \]

2. The \(x\) terms:
\[ 7x - 7x = 0 \]

3. The constant terms:
\[ -3 + 5 = 2 \]

Putting it all together, the remainder of Alex's workshop space is:

\[
2x^2 + 0 + 2 = 2x^2 + 2
\]

Thus, the expression that models the remainder of Alex's workshop space once he rents Matt his portion is:

**2x² + 2 square feet**.