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The distributive property is a fundamental idea in algebra that allows you to multiply a single term by two or more terms inside a set of parentheses. When you see something like \(a(b + c)\), you can distribute 'a' across both 'b' and 'c'. This means you perform the multiplication separately and then add the results together. For example, \(3(2 + 4)\) becomes \(3 \times 2 + 3 \times 4\), which simplifies to \(6 + 12 = 18\).

In our exercise, we used the distributive property to simplify \(-5(2-5m)\). We did this step by step: \(-5 \times 2 + (-5) \times (-5m)\). This yielded \(-10 + 25m\). Breaking it down is key; focus on distributing the multiplication to each term inside the parentheses first.

• The negative sign changes the direction of each term's multiplication.
• Even negative terms, when multiplied correctly, follow the same rules.

Remember, the distributive property can make complex expressions more manageable and easier to simplify.

Simplifying expressions means reducing them to their simplest form. This often involves combining like terms and using arithmetic to streamline the expression. Like terms are those that have the same variable raised to the same power.

For example, in our solution, after using the distributive property, we ended up with \(10 - (-10 + 25m)\). To simplify this, replace the inner terms correctly, resulting in \(10 + 10 + 25m\). Combining like terms here means adding the constant values and keeping the variables intact.

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Parentheses in algebra serve to group parts of an expression that should be treated as a single unit. They indicate the terms which need to be simplified first before dealing with other operations outside the parentheses. This is part of the order of operations (PEMDAS/BODMAS rules).

In our example, we first identified the expression inside the parentheses: \(2 - 5m\). This had to be tackled before applying the distributive property.

• Always simplify what is inside the parentheses initially.
• Then proceed with any multiplications or divisions outside the parentheses.

Correctly handling parentheses ensures that the overall expression is simplified correctly and logically. Without clear steps like these, we can mix up the order of operations and arrive at incorrect answers. Remember: clear steps and careful attention to these rules lead to accurate results.