An algebraic expression is a combination of numbers, variables, and arithmetic operations (addition, subtraction, multiplication, and division). Variables are symbols that represent unknown quantities, and they can take on different values. The expressions are often written with letters (variables) to represent the unknown values.
Examples:
3x + 5
2y – 7
4a² + 3a – 2
A term is a single part of an algebraic expression separated by addition or subtraction signs. Each term can contain constants (numbers) and variables, or just a constant by itself.
Examples:
In the expression 3x + 5, there are two terms: 3x and 5.
In the expression 2y – 7, there are two terms: 2y and -7.
In the expression 4a² + 3a – 2, there are three terms: 4a², 3a, and -2.
In a term, the coefficient is the number that multiplies the variable, and the exponent represents the power to which the variable is raised.
Examples:
In the term 3x, the coefficient is 3, and the exponent of x is 1.
In the term 4a², the coefficient is 4, and the exponent of a is 2.
Like terms are terms that have the same variables raised to the same powers. They can be combined or simplified together.
In the expression 3x + 5x, the terms 3x and 5x are like terms, and they can be combined to get 8x.
In the expression 4a² + 3a – 2a², the terms 4a² and -2a² are like terms, and they can be combined to get 2a².
To find the value of an algebraic expression for a given value of the variable, substitute the value into the expression and perform the arithmetic.
Example:
Evaluate the expression 2x + 3 for x = 4.
2(4) + 3 = 8 + 3 = 11.