In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x²-3(x-y), for x=8 and y=2

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Step 1: Start by substituting the given values of the variables into the algebraic expression. Replace x with 8 and y with 2 in the expression x^2 - 3(x - y).

Step 2: Rewrite the expression after substitution: (8)^2 - 3(8 - 2).

Step 3: Simplify the exponentiation first. Calculate 8^2, which means multiplying 8 by itself.

Step 4: Simplify the parentheses next. Subtract 2 from 8 to evaluate (8 - 2).

Step 5: Multiply the result of (8 - 2) by -3, then combine it with the result of 8^2 to simplify the entire expression.

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Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression x^2 - 3(x - y) combines these elements to represent a value based on the variables x and y. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.

Substitution

Substitution is the process of replacing variables in an expression with their corresponding numerical values. For the given expression, substituting x = 8 and y = 2 means replacing x and y in the expression to simplify and calculate the result. This technique is essential for evaluating algebraic expressions accurately.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which different operations should be performed in a mathematical expression. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), following this order ensures that calculations are performed correctly and consistently.

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x2-3(x-y), for x=8 and y=2