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The distributive property is a fundamental principle in algebra. It states that you can distribute a multiplication operation over addition or subtraction within parentheses. For example, in the expression \(a(b + c) = ab + ac\), you multiply each term inside the parentheses by the term outside the parentheses.
This property is useful because it helps in breaking down and simplifying expressions. In our exercise, we applied the distributive property to the expression \(6(m^2 - 9m + 4)\). By multiplying each term inside the parentheses by 6, we transform the expression into \(6 \times m^2 - 6 \times 9m + 6 \times 4\).
This step ensures every term inside the parentheses is appropriately scaled by the multiplier outside, making further simplification possible.

Simplifying expressions is the process of making a mathematical expression as simple as possible. This often involves combining like terms and performing basic arithmetic operations.
In our example, after using the distributive property, we have \(6 \times m^2 - 6 \times 9m + 6 \times 4\). We simplify each of these terms:

• \(6 \times m^2 = 6m^2\)
• \(6 \times 9m = 54m\)
• \(6 \times 4 = 24\)

Therefore, the simplified terms are \(6m^2, -54m,\) and \(24\).
After simplifying individual terms, we combine them to form the expression \(6m^2 - 54m + 24\).
Always recall to ensure each arithmetic operation is calculated accurately.

Elementary algebra lays the foundation for all higher mathematics. It deals with the basic rules of operations and the principles of equations and expressions.
In the given exercise, we applied elementary algebraic principles to multiply and simplify a polynomial expression.
Let's break it down:

• First, we used the distributive property to deal with the parentheses.
• Then, we simplified each term by performing basic multiplication.
• Finally, we combined all the simplified terms into a single expression.

These steps highlight critical algebraic skills such as distribution, simplification, and combining like terms.
Understanding these core concepts will aid in solving more complex polynomial equations and further enhance your mathematical problem-solving skills.