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

Verified step by step guidance

1. Step 1: Start with the given algebraic expression: $x^2\; +\; 3x$.
2. Step 2: Substitute the given value of $x\; =\; 8$ into the expression. This gives: $(8)^2\; +\; 3(8)$.
3. Step 3: Simplify the first term, $(8)^2$, which means multiplying 8 by itself.
4. Step 4: Simplify the second term, $3(8)$, which means multiplying 3 by 8.
5. Step 5: Add the results from Step 3 and Step 4 to find the value of the expression.

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression x^2 + 3x consists of the variable x raised to the second power and multiplied by 3, which are combined using addition. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. In the given problem, we substitute x with 8 in the expression x^2 + 3x. This step is crucial for evaluating the expression and obtaining a numerical result, which is a common practice in algebra.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. When evaluating the expression after substitution, following these rules is essential to arrive at the correct answer.