What do variables represent in math

It is common that many variables appear in the same mathematical formula, and they may play different roles. Some names or qualifiers have been introduced to distinguish them. Therefore, a term may simply be a constant or a variable, or it may include both a coefficient and an unknown variable. However, this is not always the case. Simplifying algebraic expressions involves combining like terms, often through addition and subtraction.

Every algebraic expression is made up of one or more terms. Terms are called like terms if they involve the same variables and exponents. All constants are also like terms. Likewise, the following are examples of like terms:.

Note that terms that share a variable but not an exponent are not like terms. Likewise, terms that share an exponent but have different variables are not like terms.

We can simplify an algebraic expression by combining like terms. When an expression contains more than two terms, it may be helpful to rearrange the terms so that like terms are together. The commutative property of addition says that we can change the order of terms without changing the meaning of the expression the sum. So, we can rearrange the order of the following expression before attempting to combine like terms:.

We want to rearrange the expression to group like terms together:. The same rules apply when an expression involves subtraction. However, be careful that when you changing the order of terms you ensure that the minus sign follows the term that it applies to. This expression is properly rearranged and simplified as follows:.

Add or subtract the coefficients of the like terms until there are as few of each kind of term as possible. Now group these like terms together:. Add and subtract the coefficients of the like terms. The expression therefore simplifies to:. A monomial is a single term consisting of a product of numbers and variables. It is a relative of the polynomial, which is an algebraic expression with more than one term.

The following are examples of monomials:. When you multiply monomials, you multiply their integer coefficients together and, if they contain any of the same variables, add the exponents on those variables together. A monomial can be multiplied by a polynomial of any size note that a polynomial is called a binomial if it has two terms and a trinomial if it has three terms. The monomial should be multiplied by each term in the polynomial separately.

Any negative sign on a term should be included in the multiplication of that term. The resulting polynomial will have the same number of terms as the polynomial in the problem.

Multiplying two binomials is less straightforward; however, there is a method that makes the process fairly convenient. The word FOIL is an acronym for the four terms of the product:. Once this process is complete, all the resulting terms are added together into a single polynomial. Remember that any negative sign on a term in a binomial should also be included in the multiplication of that term.

Additionally, remember to simplify the resulting polynomial if possible by combining like terms. A radical expression that contains variables can often be simplified to a more basic expression, much as can expressions involving only integers. Expressions that include roots are known as radical expressions.

A root of degree 2 is called a square root; a root of degree 3 is called a cube root. Roots of higher degrees are referred to using ordinal numbers e. First, look for a perfect square under the square root sign, and remove it:. For the purposes of simplification, radical expressions containing variables are treated no differently from expressions containing integers. This follows the same logic that we used above, when simplifying the radical expression with integers:.

And what the letters are, are officially called variables. A variable is a letter or a symbol used to represent any number. And it's kind of tricky because the letter is going to represent the same number within that specific problem but the same letter could represent different numbers between different problems.

Let me show you what I mean. That was like problem one on my homework. And then problem two on my homework said x take away 4 is equal to So you can probably do these in your head, think about what number x might stand for. What number plus gives you the answer 8? That's problem one. Look at problem 2. It uses the same letter but it's going to be a different number. Variables are called variables because they vary, i. Thus a variable can be considered as a quantity which assumes a variety of values in a particular problem.

Many items in economics can take on different values. Mathematics usually uses letters from the end of the alphabet to represent variables.

Economics however often uses the first letter of the item which varies to represent variables. Thus p is used for the variable price and q is used for the variable quantity. An expression such as 4x 3 is a variable.

It can assume different values because x can assume different values. In this expression x is the variable and 4 is the coefficient of x. Coefficient means 4 works together with x. Expressions such as 4x 3 which consists of a coefficient times a variable raised to a power are called monomials. A monomial is an algebraic expression that is either a numeral, a variable, or the product of numerals and variables.

Monomial comes from the Greek word, monos, which means one. Real numbers such as 5 which are not multiplied by a variable are also called monomials. Monomials may also have more than one variable. In this expression both x and y are variables and 4 is their coefficient. One or more monomials can be combined by addition or subtraction to form what are called polynomials.

Polynomial comes from the Greek word, poly, which means many. A polynomial has two or more terms i. If there are only two terms in the polynomial, the polynomial is called a binomial. The coefficients of the terms are 4, -2, and 3. The degree of a term or monomial is the sum of the exponents of the variables. The degree of a polynomial is the degree of the term of highest degree. In the above example the degrees of the terms are 5, 3, and 0.

The degree of the polynomial is 5.