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When tackling algebraic expressions, the order of operations is your best friend. It's the prioritized set of rules that you should follow to solve expressions correctly. In some places, this is known as BIDMAS, BODMAS, or PEDMAS, teaching you to handle brackets (parentheses), indices (exponents), division and multiplication, and addition and subtraction in that specific sequence.

Let's say you're working with the expression \(3(12+7)\). Your first move according to the order of operations is to solve what's inside the parentheses — it's considered the highest priority. So, you add 12 and 7 to get 19. Once you've done the work inside the brackets, you move on to the multiplication: multiplying 3 by 19 gives you 57.

• Brackets come first
• Handle each operation based on priority
• Ensure each step is followed accurately

By using the order of operations, you ensure that your solutions are consistent and correct.

The distributive property is a handy algebraic tool that helps simplify expressions, especially when dealing with multiplication over addition or subtraction. This mathematical rule allows you to "distribute" a multiplier across terms inside a bracket, making calculations flexible and often easier.

In the expression \(3(12+7)\), you can expand it using the distributive property. This means you multiply 3 by each of the numbers inside the parentheses separately. So, calculate \(3 \times 12\) to get 36, then calculate \(3 \times 7\) to get 21. Finally, you add these products together: 36 plus 21 equals 57.

• Distribute the multiplier over each term inside the brackets
• Multiply separately then add the results
• Makes handling larger expressions straightforward

Using the distributive property can make it easier to mentally compute expressions.

Mathematical expressions are combinations of numbers, variables, and operators that represent a particular value or relationship. They form the language of algebra, allowing us to express complex problems in a more manageable form.

The expression \(3(12+7)\) is a simple yet effective example illustrating how expressions work. This expression includes a bracketed term and a multiplier, showcasing the use of different operators that guide you in solving for a final value.

• Compositions of numbers and operations
• Can include variables, constants and operators
• Require understanding of mathematical rules

Understanding how to interpret and solve mathematical expressions is a fundamental skill in algebra that translates to solving real-world problems with mathematical clarity.