91Ó°ÊÓ

Algebraic expressions are a combination of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. They represent mathematical relationships in a compact form. A key aspect to grasp is how they can be manipulated to find the value of an unknown by performing various operations.
For instance, in the expression \( yz - y^2 \), we see two algebraic components: \( yz \) and \( y^2 \). Each part signifies different operations involving the variables \( y \) and \( z \).

• \( yz \) implies multiplication of the values of \( y \) and \( z \).
• \( y^2 \) signifies the squaring of the value of \( y \).

Algebraic expressions allow us to model real-world situations mathematically and provide a foundation to solve them. Evaluating these expressions for specific values, as in our exercise, can uncover patterns and insights in various fields.

Variable substitution is the process of replacing variables in an algebraic expression with their actual given values. This is an important step when solving an expression or equation, as it transforms the abstract expression into a numerical form that can be calculated.
In our example, we are given the values \( y = -5 \) and \( z = 0 \). Replacing \( y \) and \( z \) in the expression \( yz - y^2 \) involves:

• Substituting \( -5 \) in place of \( y \).
• Substituting \( 0 \) in place of \( z \).

After substitution, the expression becomes \( (-5) \times 0 - (-5)^2 \). This process simplifies the evaluation as it turns variables into concrete numbers, facilitating further arithmetical computations.

Order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to correctly solve an expression. Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), following these rules ensures that we reach the correct solution.
For the expression \( (-5) \times 0 - (-5)^2 \), we need to:

• First, calculate the multiplication \((-5) \times 0\) which gives \( 0 \).
• Then, calculate the exponentiation \((-5)^2\) which results in \( 25 \).
• Finally, perform the subtraction \(0 - 25\) to get \(-25\).

By applying the order of operations meticulously, we ensure that each step is executed correctly, leading us to the accurate result of the evaluated expression.