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:
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The \(x^2\) terms: \[ 4x^2 - 2x^2 = 2x^2 \]
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The \(x\) terms: \[ 7x - 7x = 0 \]
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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.