91Ó°ÊÓ

The distributive law in algebra helps you to simplify complex expressions and is a fundamental tool in mathematics. It states that when you multiply a number by a sum, you can distribute the multiplication over each addend within the parentheses. The rule can be written as \( a(b + c) = ab + ac \). This can make calculations easier and expressions simpler.

For instance, in the expression \( 2(5x + 4) \), you apply the distributive law by multiplying \( 2 \) with each term inside the parentheses. This means \( 2 \) is multiplied by \( 5x \) and then by \( 4 \). By distributing, the expression becomes \( 2 \times 5x + 2 \times 4 \), which simplifies to \( 10x + 8 \).

Using the distributive law helps in simplifying expressions to a form that is easier to work with. It is particularly useful when solving equations and can save time and reduce errors.

Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. It's like a language for expressing mathematical ideas. By using variables, we can express general relationships and be able to solve for unknown values.

When simplifying algebraic expressions, the goal is to make them as simple as possible. This involves combining like terms, using the distributive law, and performing basic operations like addition and subtraction. In our exercise, we started with \( 2(5x + 4) - 3 \). After applying the distributive law, we transformed it into \( 10x + 8 \).

Algebra allows us to handle more complex problems efficiently. By mastering algebraic techniques, you unlock the potential to solve a wide range of mathematical problems. It is essential to practice and understand each step to become proficient.

Constant subtraction is another fundamental concept in algebra when you have an equation or expression to simplify. After distributing, you often get a simpler expression, but there's usually one more step to complete: dealing with any constant terms.

In our given expression \( 10x + 8 - 3 \), the last part involves subtracting the constant \( 3 \) from \( 8 \). The subtraction is straightforward: you simply subtract the numbers. Here, \( 8 - 3 \) equals \( 5 \), so the expression simplifies to \( 10x + 5 \).

Subtracting constants helps to bring the expression to its simplest form. By performing these basic operations correctly, you ensure that your final result is as simplified as possible, making further calculations easier and more accurate.