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The distributive property is a fundamental concept in algebra that helps simplify expressions. It allows us to remove parentheses by distributing a multiplication across terms within them. Here's how it works:

In the expression \(-2(a+7)\), the distributive property tells us to multiply \(-2\) by each term inside the parentheses. This means:

• Multiply \(-2\) by \(a\), which gives \(-2a\).
• Multiply \(-2\) by \(7\), which gives \(-14\).

By applying this principle, you can break down complex expressions into simpler components, making them easier to work with. This method not only simplifies but also ensures accuracy in calculations by breaking them into manageable parts.

Once you have distributed the terms, the next step is to combine like terms. Like terms are terms in an algebraic expression that have the same variable raised to the same power. In our simplified expression \(-2a - 14\), it's important to look for terms that can be combined.

In this case, we only have one type of variable term \(-2a\), and the other term is a constant \(-14\). Since there are no similar variable terms to combine \(-2a\) with, and because \(-14\) is already simplified as a constant, we keep them as they are. The expression doesn't need further simplification with respect to like terms, which means you're all done! Remember, combining like terms reduces expressions to their simplest form, ensuring clarity and ease of use in solving equations.

Multiplication is a core operation in algebra that often intertwines with the distributive property. In algebra, multiplication involves both numbers and variables. When multiplying terms, keep these points in mind:

• Sign rules apply: A negative times a positive is negative, which is evident in \(-2 \times 7 = -14\).
• Variables follow the basic multiplication rules: Multiplying \(-2\) by \(a\) gives \(-2a\).

Multiplication in algebra isn't just about computing numbers—it's a tool for transforming expressions through the distributive property. It allows for the reorganization and decomposition of terms to simplify and solve problems effectively. Once you grasp multiplication's role, it becomes a powerful ally in tackling diverse algebraic challenges.