Question

As part of your role, you are tasked with designing a new quarter pipe ramp that will require a cubic equation to model its shape accurately. You start by using your knowledge of cubic equations to come up with a general formula:

(m − 3)(m² + 3m − 4)

You will need to simplify the expression so that you can continue to refine the design of the ramp.

Answer 1

To simplify the cubic equation (m - 3)(m² + 3m - 4), we distribute the terms to get m³ + 3m² - 4m - 3m² - 9m + 12, then combine the like terms to arrive at m³ - 13m + 12.

Step-by-step explanation:

To simplify the cubic equation given by the product (m - 3)(m² + 3m - 4), we need to distribute the terms. The multiplication will result in the standard form of a cubic equation that can better describe the shape of the quarter pipe ramp. Here's how you simplify the expression:

First, apply the distributive property:
m(m²) + m(3m) + m(-4) - 3(m²) - 3(3m) - 3(-4)

Next, perform the multiplications:
m³ + 3m² - 4m - 3m² - 9m + 12

Combine like terms:
m³ - 4m - 9m + 12
m³ - 13m + 12

Now, we have the simplified cubic equation m³ - 13m + 12 which can assist in the ramp design process.