(m+3)(m^2+3m+5)

Jasonbradley

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Jun 16, 2024

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Multiplying Polynomials: (m+3)(m^2+3m+5)

This article will guide you through the process of multiplying the two polynomials: (m+3)(m^2+3m+5).

Understanding the Concept

To multiply polynomials, we use the distributive property. This means we multiply each term in the first polynomial by every term in the second polynomial.

Step-by-Step Solution

1. Expand the first polynomial: (m+3) remains as it is.

2. Expand the second polynomial: (m^2 + 3m + 5) remains as it is.

3. Multiply each term in the first polynomial by every term in the second polynomial:

   • m * m^2 = m^3
   • m * 3m = 3m^2
   • m * 5 = 5m
   • 3 * m^2 = 3m^2
   • 3 * 3m = 9m
   • 3 * 5 = 15

4. Combine like terms: m^3 + 3m^2 + 5m + 3m^2 + 9m + 15 = m^3 + 6m^2 + 14m + 15

Final Answer

Therefore, the product of (m+3)(m^2+3m+5) is m^3 + 6m^2 + 14m + 15.