91Ó°ÊÓ

The distributive property is a fundamental rule in algebra that allows us to multiply a single term by each term within a parenthesis and then sum the results. For instance, when faced with an expression like \( a(b + c) \), we can ‘distribute’ the \( a \) across the terms within the parentheses, giving us \( ab + ac \).

Let’s consider an example from our exercise \( 12x(x+2) \). When applying the distributive property, we multiply \( 12x \) by each term inside the parenthesis: \( x \) and \( 2 \). This simplification step results in \( 12x^2 + 24x \), which are then combined to give a clearer and more concise expression.

Algebraic expressions are combinations of variables, numbers, and arithmetic operations. Variables, often represented by letters such as \( x \) or \( y \), can take various values, making algebra an essential tool for solving a myriad of problems. For example, our initial algebraic expression \( 16x \) involves the multiplication of a variable \( x \) by 16, indicating the variable amount multiplied by 16.

In the context of our problem-solving exercise, to simplify an algebraic expression means to perform all possible arithmetic operations. In the given exercise, we first identified the expressions and then applied the distributive property to one of them to make it simpler and more straightforward.

Elementary algebra is the branch of mathematics that deals with the manipulation and solution of equations involving variables. It’s a gateway into more complex areas of mathematics and everyday problem-solving. Starting from basic concepts such as adding, subtracting, multiplying, and dividing numbers, it progresses to include operations with variables that can represent numbers in general terms.

The steps we encountered in our exercise represent the basic essence of elementary algebra. Step 1 required us to identify the expressions, a crucial skill in recognizing the components we are working with. Step 2 involved simplifying the second term using the distributive property, a key technique in algebraic manipulation. The final step was writing the answer in a simplified form, which encapsulates the goal of algebra: expressing complex relationships in the simplest form possible.