Mr. Moore had to find the area of a flower bed in his yard so he knew how much mulch to purchase. Below is a picture of his yard and the work he did to find the area.

Area = (2x^2-3x^3)^2

Step1: (2x^2)^2 - (3x^3)^2

Step 2: 4x^4-9x^6
Final answer is 4x^4-9x^6 feet^2

Part A: Explain in detail the error that was made above

Part B: Choose the correct formula to solve the problem

Part C: Put the steps in order to solve the problem correctly.

Part D: The units fpr the final answer would be:

1 answer

Part A:
The error in the solution provided above is in Step 1. When expanding the equation (2x^2-3x^3)^2, the correct way to do so is by using the formula (a-b)^2 = a^2 - 2ab + b^2. Therefore, the correct expansion should be (2x^2)^2 - 2(2x^2)(3x^3) + (3x^3)^2, which would result in the correct answer.

Part B:
The correct formula to solve the problem is (a-b)^2 = a^2 - 2ab + b^2.

Part C:
1. Expand the equation (2x^2-3x^3)^2 using the formula (a-b)^2 = a^2 - 2ab + b^2
2. (2x^2)^2 - 2(2x^2)(3x^3) + (3x^3)^2
3. Simplify the equation to get the final answer 4x^4 - 12x^5 + 9x^6 feet^2

Part D:
The units for the final answer would be feet^2, as it represents the area of the flower bed in square feet.