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One of the foundational bricks in algebra is the distributive property. It's a rule that allows you to multiply a single term by each term within a parenthesis. For instance, take the expression given in the exercise, where we have the term 2 to be distributed across the two terms inside the parenthesis: 5x and 4. To apply the distributive property effectively, you multiply the term outside the parenthesis (in this case, 2) by each term inside separately: 2 times 5x and 2 times 4.

• 2(5x) becomes 10x,
• 2(4) becomes 8.

Once these multiplications are carried out, you merge the results into a single algebraic expression, which gives us 10x + 8 in the example. Grasping this concept can help solve numerous algebra problems and is a major step in your journey of mastering algebraic expressions.

Arithmetic operations form the core of dealing with numbers, and they hold equal importance in algebra. These operations include addition, subtraction, multiplication, and division and operate under specific rules when applied to algebraic expressions. For algebra, it's more than just computing values; it's about understanding how these operations interact with variables.

In algebra, you follow the same order of operations as in arithmetic, commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the context of our exercise, once we’ve distributed and combined like terms, the last operation left to perform is subtraction. Subtraction is the last step in simplifying the given expression. The provided example concludes with subtracting 3 from the sum of 10x + 8 which results in the final simplified expression of 10x + 5.

Algebraic expressions can seem daunting at first glance, but breaking them down into steps can make them much more manageable. Let's take a closer look at the step-by-step process highlighted by the example provided.

The simplification starts with distribution, as mentioned before. Once the terms are distributed, it's vital to combine like terms – terms that have the same variables raised to the same power. In the exercise, after distribution, we do not have like terms to combine, so we move to the next step. We then apply the appropriate arithmetic operations in the correct order. In this case, it's a simple subtraction of numerals. Each step brings the algebraic expression to a simpler form, making it easier to understand and, if needed, solve if it were an equation. The goal is to represent the expression in the most concise and straightforward way possible, and following these step-by-step procedures helps in achieving that.

Remember, practice these steps consistently, and soon you'll find that simplifying algebraic expressions has become second nature.