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 2x2−8 square feet 2 x squared minus 8 square feet 6x2+14x−8 square feet 6 x squared plus 14 x minus 8 square feet 2x2+2 square feet 2 x squared plus 2 square feet 2x2−14x−8 square feet

Answer 1

To find the expression that models the remainder of Alex's workshop space after renting a portion to Matt, we need to subtract the area of the space rented to Matt from the total area of the workshop.

The area of Alex's workshop is given by:

\( 4x^2 + 7x - 3 \)

And the area rented to Matt is:

\( 2x^2 + 7x - 5 \)

Now, let's perform the subtraction:

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

Distributing the negative sign to the second expression:

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

Now we can combine like terms:

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

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

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

Putting it all together, the expression for the remaining space is:

\[
2x^2 + 2
\]

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

**2x² + 2 square feet**.