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The distributive property is a crucial concept in algebra that allows us to simplify expressions efficiently. Essentially, it involves distributing, or multiplying, an outer term to each of the terms within a set of parentheses. This property is commonly written as \(a(b + c) = ab + ac\). By applying the distributive property, we can transform expressions into simpler, more manageable forms.

In the context of the original exercise, we start with \[-3a(5a-6)\].
To apply the distributive property here, we multiply -3a by each component inside the parentheses.
This method allows us to evaluate each term independently before combining them into a single expression.

• Multiply -3a by 5a.
• Multiply -3a by -6.

By handling each multiplication separately, we leverage the distributive property to methodically break down and simplify the expression.

Multiplying algebraic terms may seem intimidating at first, but it becomes straightforward once you understand the rules. When multiplying terms, especially in expressions that involve variables, we follow specific steps:

• Multiply the coefficients (numerical parts) of the terms.
• Multiply the variables by adding their exponents if they are the same.

Using the example from the exercise, -3a is first multiplied by 5a:
\(-3a \times 5a = -15a^2\).
Here, -3 and 5 are coefficients that multiply to give -15, and a and 5a give a^2 by adding their exponents, which is 1 + 1.

Next, we take -3a and -6:
\(-3a \times -6 = 18a\).
The negative signs cancel out, resulting in a positive value.
So -3 times -6 becomes 18, and a is left as a since it's only a multiplication by itself.
Grasping the principles of multiplying terms will make solving algebraic expressions much easier.

Simplifying expressions is the process of transforming them into their simplest form, making them easier to understand and work with.
This involves reducing terms, combining like terms, and sometimes, even factoring.

Let's see how the original exercise wraps up simplification.
After applying the distributive property and multiplying the terms, we obtained:
\(-15a^2 + 18a\).
Both terms, \(-15a^2\) and \(18a\), are in their simplest form because:

• They cannot be further combined due to having different exponents on a.
• There are no common factors or like terms left to factor out or simplify.

By simplifying expressions, we achieve a structured expression that clearly conveys the solution with all calculations properly resolved.
Simplifying not only aids in understanding but also paves the way for solving more complex equations efficiently.