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−2)(m²+2m−3)

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

Answer 1

The cubic equation (m-2)(m² + 2m - 3) is simplified by distributing (m-2) across the quadratic then combining like terms to yield m³ - 6m + 6.

Step-by-step explanation:

To begin designing the quarter pipe ramp, you need to simplify the given cubic equation (m-2)(m² + 2m - 3). The simplification process involves expanding the brackets and combining like terms. Let's go through the steps to simplify the expression:

1. Multiply the term (m-2) by each term in the quadratic (m² + 2m - 3).
2. You'll get three products: (m-2)*m², (m-2)*2m, and (m-2)*(-3).
3. Distribute (m-2) across each term: m³ - 2m² + 2m² - 4m - 3m + 6.
4. Combine like terms to get the simplified cubic equation: m³ - 6m + 6.

Now, you can use this simplified equation to refine the design of your quarter pipe ramp.