An algebraic expression is a mathematical phrase that includes numbers, variables (such as $x$, $y$, or $z$), and operational symbols (such as $+, -, \times,$ and $\div$). These expressions represent values without requiring an equal sign as in equations. Here’s a quick breakdown:

1. Terms: The parts of an algebraic expression separated by $+$ or $-$ signs. Each term can be a constant, a variable, or a product of constants and variables. For instance, in $3x + 5y - 7$, $3x$, $5y$, and $-7$ are terms.

2. Constants: Fixed values in an expression, like the $-7$ in $3x + 5y - 7$.

3. Variables: Symbols that represent unknown numbers, like $x$ and $y$ in the expression $3x + 5y - 7$.

4. Coefficients: Numbers multiplying variables. In $3x + 5y - 7$, the coefficient of $x$ is $3$ and for $y$, it is $5$.

5. Operations: Addition, subtraction, multiplication, or division are performed on terms.

An example of an algebraic expression is: $4x^2 + 3y - 8$ where $4x^2$ is one term, $3y$ is another, and $-8$ is a constant term.

Would you like to go through more examples or solve an expression?

Here are some related questions:

1. How do you simplify an algebraic expression?
2. What is the difference between an equation and an expression?
3. How do you evaluate an algebraic expression for specific values?
4. What is the distributive property in algebraic expressions?
5. Can algebraic expressions include exponents or roots?

Tip: Remember, combining like terms (terms with the same variable and exponent) is essential in simplifying expressions!