The expression is composed of the sum of , , and :
Each of , , and is called a term of .
A term composed solely of a number, such as , is called a constant term.
In a term like , the number , which is multiplied by the variable , is called the coefficient of .
Expressions made up of one or more terms, such as or , are called polynomials. A polynomial with only one term is referred to as a monomial.
For example, represents , a term with one multiplied, while represents , a term with two 's multiplied.
The degree of a term is the number of times a variable is multiplied in that term.
The degree of a polynomial is the degree of the term with the highest degree.
Specifically, a polynomial of degree is called a linear expression.
Multiplication and Division of Linear Expressions
For the monomial and the number , their product is calculated as follows using the commutative and associative properties of multiplication:
Thus, when multiplying a monomial by a number, the numbers are multiplied together, and the result is placed before the variable.
For division, dividing a monomial by a number is equivalent to multiplying by the reciprocal of the divisor, as with regular division.
When multiplying a linear expression by a number, the distributive property is applied to multiply the number by each term in the expression:
Similarly, dividing a linear expression by a number is done by multiplying by the reciprocal of the divisor:
Addition and Subtraction of Linear Expressions
Terms with the same variable raised to the same power are called like terms. For example, all constant terms are like terms.
Polynomials containing like terms can be simplified by combining the like terms using the distributive property:
To add linear expressions, group like terms and combine them.
If parentheses are present, remove them first, then combine like terms.
To subtract linear expressions, change the sign of each term in the subtracted expression and then perform addition.