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.
StepbyStep Solution

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

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

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

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.