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The distributive property is a helpful tool in algebra that allows you to distribute multiplication over addition or subtraction within parentheses. It is especially useful when you need to simplify expressions.
For instance, when you have an expression like \(-5(z+3)\), the distributive property lets you multiply \(-5\) with each term inside the parentheses separately.

• Multiply \(-5\) by \(z\), resulting in \(-5z\).
• Multiply \(-5\) by \(+3\), resulting in \(-15\).

So, \(-5(z+3)\) equals \(-5z - 15\). This method is essential because it simplifies the expression, allowing further steps like combining like terms.
Using the distributive property effectively can make complex expressions much easier to work with and understand.

Once you have used the distributive property, the next step is usually to combine like terms. Like terms are terms in an expression that have the same variable raised to the same power.
Let’s look at our example after distribution: \(-5z - 15 + 2z\).

• Identify like terms: Here, \(-5z\) and \(+2z\) are like terms because they both contain the variable \(z\).
• Combine them by adding their coefficients: \(-5 + 2\) gives us \(-3\), so \(-5z + 2z = -3z\).

Don't forget about the constant term \(-15\).
This approach helps to reduce the expression to a simpler form, which is often your goal in algebra. By combining like terms, you consolidate your expression, making it easier to understand and solve.

Algebraic expressions are mathematical phrases composed of numbers, variables, and operational symbols. Simplifying these expressions involves a few key steps that make them easier to understand and work with.
In our example, the original algebraic expression was \(-5(z+3) + 2z\).

• Each part of the expression can include coefficients (numerical parts) and variables (like \(z\)).
• An algebraic expression may also include constant numbers like \(-15\), which are terms without variables.

Through processes like applying the distributive property and combining like terms, we transform the expression into a more manageable form: \(-3z - 15\).
This final simplified version retains the same value as the original expression but is easier to interpret and use in calculations. Understanding how to manage algebraic expressions is a fundamental skill that facilitates solving more complex algebraic equations and real-world problems.