Question

A painter has already painted one wall. The area of the first wall is modeled by ​4x​ 2 ​ + 12x + 9​, and the area of the both walls is modeled by ​36x​ 2 ​ - 12x + 1​. What is the area of the remaining wall space that he needs to finish painting? How do you combine like terms and show your work correctly.

Answer 1

The area of the remaining wall that needs painting is found by subtracting the area of the first wall from the total area of both walls, resulting in an algebraic expression of 32x2 - 24x - 8.

Step-by-step explanation:

The question outlines two algebraic expressions representing the areas of two walls. The first wall has an area of 4x2 + 12x + 9 and the combined area of both walls is 36x2 - 12x + 1. To find the area of the second wall that remains to be painted, we need to subtract the area of the first wall from the total area of both walls.

We achieve this by combining like terms and performing algebraic subtraction:

First, rewrite the total area of both walls and the area of the first wall side by side:36x2 - 12x + 1 (Total area of both walls)-(4x2 + 12x + 9) (Area of the first wall to be subtracted)Perform the subtraction to find the area of the second wall:36x2 - 12x + 1- 4x2 - 12x - 9= 32x2 - 24x - 8 (Area of the second wall)

Hence, the area of the remaining wall space that needs to be painted is 32x2 - 24x - 8.