Alex has a workshop with an area that can be modeled by the expression 4x^2+7x−3

Question

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 2x^2+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

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

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

2x^2+2
square feet
2 x squared plus 2 square feet

2x^2−14x−8
square feet
2 x squared minus 14 x minus 8 square feet
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Answer 1

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

1. Total area of Alex's workshop: \[ 4x^2 + 7x - 3 \]

2. Area Matt is renting: \[ 2x^2 + 7x - 5 \]

Now, we will subtract Matt’s area from Alex’s total area:

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

Distributing the subtraction:

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

Now, 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 remainder of Alex's workshop is:

\[ 2x^2 + 2 \]

Thus, the correct answer is:

2x^2 + 2 square feet.