A family is building a rectangular patio in their backyard. The rectangular yard has dimensions of (8x+2) by (6x + 3) and they are planning the patio to be (x + 5) by (3x + 1). What is the area of the remaining yard after the patio has been built?

yard

48 x^2 + 36 x + 6

patio

3 x^2 + 16 x + 5

subtract

45 x^2 + 20 x + 1

Polynomials and Factoring Unit

1. 13x^10
2. -7y^5
3. 6x^2 + 2x + 8 - quad tri.
4. 11x^2 + 0.7x + 8.2
5. 78x^2
6. 15p^2 + 7p - 2
7. 15h^2 + 42h + 24
8. FOIL 18x^2 - 30x + 8
9. 80x^3+144x^2+84x+16
10. 16x^2-48xy^3+36y^6
11. (x + 6 and x - 2)
12. (x + 6 and x - 5)
13. (x-6y and x-4y)
14. (5x+4 and 2x-1)
15. (3x+5 and x-6)
16. 45x^2 + 20x + 1 - Patio
17. (w+6)^2
18. (r-7 and r+7)

walmart lied

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Just took the test this is 100% trust me if you want.

Don't listen to coolkid or AI5X1, all the questions are in a different order for everyone so you can't get the right answers based on letters

do you have the rest of the answers to the test ?

idk who's correct and who isn't

To find the area of the remaining yard after the patio has been built, we need to find the area of the entire yard and subtract the area of the patio.

First, let's find the area of the entire yard:
Area of the yard = length × width

Given that the length of the yard is (8x + 2) and the width of the yard is (6x + 3), we can write the equation as:
Area of the yard = (8x + 2) × (6x + 3)

Expanding this equation, we get:
Area of the yard = 48x^2 + 24x + 12x + 6
Area of the yard = 48x^2 + 36x + 6

Next, let's find the area of the patio:
Area of the patio = length × width

Given that the length of the patio is (x + 5) and the width of the patio is (3x + 1), we can write the equation as:
Area of the patio = (x + 5) × (3x + 1)

Expanding this equation, we get:
Area of the patio = 3x^2 + x + 15x + 5
Area of the patio = 3x^2 + 16x + 5

Now, we can subtract the area of the patio from the area of the yard to find the area of the remaining yard:
Area of the remaining yard = Area of the yard - Area of the patio

Substituting the equations we found earlier:
Area of the remaining yard = (48x^2 + 36x + 6) - (3x^2 + 16x + 5)

Simplifying this equation, we get:
Area of the remaining yard = 48x^2 - 3x^2 + 36x - 16x + 6 - 5
Area of the remaining yard = 45x^2 + 20x + 1

Therefore, the area of the remaining yard after the patio has been built is 45x^2 + 20x + 1.

coolkid is right! 100% on the test!

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i know this looks unreliable i am sorry but it is reliable