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The distributive property is a fundamental rule in algebra that lets you multiply a term across an expression in parentheses. It simplifies expressions by distributing a single multiplier to each term inside the parenthesis.

For example, if you have an expression like \[a(b + c)\] then it can be expanded using the distributive property to:

• \(a \times b\)
• \(a \times c\)

Combining these two products, the expression becomes \(ab + ac\).

In the problem \[-2(-y + 9)\],this rule is used to multiply \(-2\) by every term inside the parentheses:

• \(-2 \times -y = 2y\)
• \(-2 \times 9 = -18\)

So, the simplified expression after applying the distributive property is \(2y - 18\).
Understanding this property allows you to handle multiplication across parentheses with ease.

Negative numbers can sometimes be tricky to work with, especially in multiplication. They follow certain rules that help in simplifying expressions.

Here are some key points:

• When you multiply two negative numbers, the result is a positive number.
• A negative times a positive results in a negative.

In our example:

• Multiplying \(-2\) with \(-y\) gives \(2y\). Here, the product becomes positive because two negatives are multiplied.
• Multiplying \(-2\) with \(9\) yields \(-18\), because we have a negative times a positive.

Remembering these rules helps ensure you get the signs right during simplification.

Algebraic expressions consist of variables, numbers, and operators (like addition and multiplication). They are at the heart of algebra and must be understood well. Analyzing and simplifying these expressions are essential skills.

In the given problem, the original expression \[-2(-y + 9)\]is considered an algebraic expression because it includes a variable \(y\), numbers, and multiplication.

To simplify such expressions, you typically:

• Apply rules like the distributive property.
• Combine like terms if possible.

For this problem, the process of multiplying becomes straightforward after the application of the distributive property. The expression \(2y - 18\) is already simplified, meaning there are no like terms left to combine.

Understanding how algebraic expressions work builds your foundation in algebra, enabling you to solve more complex equations as you progress.