Question

A carpenter is refinishing two cupboards. She must add the areas of the cupboards to determine the amount of plywood she needs. The area of the first cupboard is modeled by 3a^2 − 5y + 15, and the area of the second cupboard is modeled by 4a^2 + 5y + 5. Identify the polynomial that represents the total area of the cupboards.

Answer 1

You are given the area of both cupboards.

The total area would be found by adding the two areas together:

3a^2 − 5y + 15 + 4a^2 + 5y + 5

Combine like terms:

3a^2 + 4a^2 = 7a^2

-5y + 5y = 0y

15 +5 = 20

The area of both cupboards would be 7a^2+20

Answer 2

The polynomial that represents the total area of the cupboards is $7a^{2} + 20$

How to identify the polynomial that represents a quantity-

Given that the area of first cupboard is =  $3a^{2} - 5y + 15$

And the area of second cupboard is =  $4a^{2} + 5y + 5$

Therefore the total area of the cupboard is represented as the sum of the area of first and second cupboard.

   Total area = Area of cupboard 1 + Area of cupboard 2

⇒ Total area = $3a^{2} - 5y + 15 + 4a^{2} + 5y + 5$

                    = $3a^{2} + 4a^{2} - 5y + 5y + 15 + 5$

∴  Total area = $7a^{2} + 20$

To learn more about polynomial expressions, refer -

https://brainly.com/question/10726042

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