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The distributive property is a fundamental principle in algebra that allows us to simplify complicated expressions by removing parentheses. It involves multiplying a single term, known as the coefficient, by each term inside the parentheses. In simpler terms, when you have something like \(a(b + c)\), the distributive property lets you rewrite it as \(ab + ac\). This can make handling expressions much easier, especially when simplifying.
Let's take a look at an example from our original exercise. We started with \(3(x + 2)\) and used the distributive property to multiply 3 by each term inside the parentheses. This resulted in \(3 \times x + 3 \times 2\), which equaled \(3x + 6\). By applying this property, you simplify expressions in a structured way. It's a useful tool to master when handling more complex algebraic problems.

Once you've distributed and expanded the expression, the next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. They are important because only like terms can be added or subtracted from one another in algebra.
In the expression \(3x + 6 - 11x\), note that \(3x\) and \(-11x\) are like terms since they both involve the variable \(x\).

• \(3x\) represents three units of \(x\).
• \(-11x\) represents a reduction of eleven units of \(x\).

By combining them, you subtract 11 from 3, resulting in \(-8x\). The number 6 has no variable and remains unchanged as there are no other constant terms to combine it with. The simplification gives you \(-8x + 6\). This process is crucial and solidifies the final expression with the least number of terms.

Algebraic expressions are central to solving algebra problems. They consist of numbers, variables, and operators (like addition or multiplication) that together represent specific values or relationships. These expressions do not have an equal sign and can vary in complexity from simple to quite complicated.
In our example, \(3(x + 2) - 11x\) is an algebraic expression involving a variable \(x\).

• Expressions can include one or more variables.
• They often contain unknown values denoted by letters (in most cases \(x, y, z\)).
• The operations that connect the numbers and variables define the expression's structure.

The power of algebraic expressions comes from their ability to model real-life scenarios and find solutions to equations. By understanding how to manipulate and simplify them, such as through distribution and combining like terms, you can tackle a wide range of mathematical problems with confidence.