Algebraic expressions are combinations of numbers, variables like x or y, and mathematical operations such as addition, subtraction, multiplication, and division. For example, 3x plus 5 is an algebraic expression. These expressions are used to represent mathematical relationships and can be evaluated by substituting specific values for the variables.
Let's break down the components of an algebraic expression. In the expression 3x plus 5, we have a variable x, a coefficient 3 which multiplies the variable, and a constant term 5. Variables are symbols that represent unknown values, coefficients are numbers that multiply variables, and constants are fixed numbers that don't change.
Algebraic expressions are classified based on the number of terms they contain. A monomial has one term, like 5x. A binomial has two terms, like 3x plus 2. A trinomial has three terms, like x squared plus 3x plus 2. And a polynomial has many terms, like 4x cubed minus 2x squared plus x minus 7.
To evaluate an algebraic expression, we substitute the given values for variables and then perform the operations. For example, to evaluate 3x plus 5 when x equals 2, we first substitute 2 for x, getting 3 times 2 plus 5. Then we perform the multiplication to get 6 plus 5. Finally, we add to get the result 11.
Simplifying algebraic expressions involves combining like terms. Like terms are terms that have the same variables raised to the same powers. In the expression 3x plus 2x plus 5, the terms 3x and 2x are like terms because they both contain the variable x. We can combine them by adding their coefficients: 3 plus 2 equals 5, so the simplified expression is 5x plus 5.