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
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Answer 1

To find the expression that models the remainder of Alex's workshop space once he rents Matt his portion, we need to subtract the area of Matt's space from the area of Alex's workshop.

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

The area of Matt's space is:
\[ 2x^2 + 7x - 5 \]

Now we perform the subtraction:

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

Distributing the negative sign:

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

Now, combine like terms:

1. Combine \( 4x^2 - 2x^2 = 2x^2 \)
2. Combine \( 7x - 7x = 0 \)
3. Combine \( -3 + 5 = 2 \)

Putting it all together:

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

Thus, the expression that models the remainder of Alex's workshop space is:

\[
\boxed{2x^2 + 2} \text{ square feet}
\]