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 expression (m-3)(m²+3m-4), multiply each term of the second expression by (m-3) and then combine like terms. The final result is the cubic expression m³ - 13m + 12.

Step-by-step explanation:

To simplify the cubic expression (m-3)(m²+3m-4), we need to distribute the first term (m-3) to each term of the second quadratic expression (m²+3m-4). We follow these steps:

1. Multiply (m-3) by m² to get m³.
2. Multiply (m-3) by +3m to get +3m².
3. Multiply (m-3) by -4 to get -12m.
4. Combine like terms.

After performing these operations, we obtain the expanded form: m³ - 3m² + 3m² - 9m - 4m + 12.

Now, we combine like terms -3m² + 3m², which cancel each other out, and -9m - 4m, which simplify to -13m. The final simplified cubic expression is m³ - 13m + 12.