Factoring and Expanding (m2)(m1)(m+3)
This expression represents the product of three linear factors: (m2), (m1), and (m+3). We can approach it in two ways:
1. Expanding the Expression
We can expand the expression by multiplying the factors step by step:

Multiply the first two factors: (m2)(m1) = m²  m  2m + 2 = m²  3m + 2

Multiply the result by the third factor: (m²  3m + 2)(m+3) = m³ + 3m²  3m²  9m + 2m + 6 = m³  7m + 6
Therefore, the expanded form of (m2)(m1)(m+3) is m³  7m + 6.
2. Finding the Roots
The expression (m2)(m1)(m+3) is equal to zero when any of the factors are equal to zero. This leads to the following solutions:
 m  2 = 0 => m = 2
 m  1 = 0 => m = 1
 m + 3 = 0 => m = 3
Therefore, the roots of the equation (m2)(m1)(m+3) = 0 are m = 2, m = 1, and m = 3.
Applications
Understanding how to factor and expand expressions like (m2)(m1)(m+3) is crucial in various mathematical fields, including:
 Algebra: Solving equations, simplifying expressions, and understanding the relationship between factors and roots.
 Calculus: Finding derivatives and integrals of polynomial functions.
 Linear Algebra: Working with matrices and vectors.
In addition to its mathematical significance, understanding the factorization and expansion of expressions like this can also be helpful in other areas such as:
 Physics: Modeling physical phenomena using equations.
 Engineering: Designing and analyzing structures and systems.
 Computer Science: Developing algorithms and data structures.
Overall, understanding the relationship between factored and expanded forms of expressions provides a valuable tool for solving various mathematical problems and understanding the underlying principles of many scientific and engineering fields.