Algebraic Expressions

An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It's only a phrase, not the whole sentence, so it doesn't include an equal sign.
Algebraic expression:
3x2 + 2y + 7xy + 5In an algebraic expression, terms are the elements separated by the plus or minus signs. This example has four terms, 3x2, 2y,7xy, and 5. Terms may consist of variables and coefficients, or constants.

In algebraic expressions, letters represent variables. These letters are actually numbers in disguise. In this expression, the variables are x and y. We call these letters "variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression.

Coefficients are the number part of the terms with variables. In3x2 + 2y + 7xy + 5, the coefficient of the first term is 3. The coefficient of the second term is 2, and the coefficient of the third term is 7.
If a term consists of only variables, its coefficient is 1.


A monomial is an algebraic expression consisting of only one term like external image monomios4.gif , where a is said to be the coefficient.

Like terms, or similar terms, are terms which differ only in numerical coefficients

Addition of monomials .
Addition of like terms is achieved by combining the numerical coefficients. external image monomios3.gif

Subtraction of monomials .
Subtraction of like terms is achieved by subtracting the numerical coefficients. external image monomios2.gif

Multiplication of monomials.
To multiply two or more monomials, multiply the numerical coefficients and multiply the variables. Don't forget the laws of exponents, the rule of signs, and the commutative and associative properties of multiplication

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Division of monomials.
To divide a monomial by a monomial, find the quotient of the numerical coefficients, find the quotients of the variables and multiply these quotients

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Addition of polinomials
Adding polynomials is essentially combining like terms of polynomial expressions. When adding polynomials, they can either be arranged vertically or grouped according to degree.

Subtraction of polynomials.
Subtraction of two algebraic expressions is achieved by changing the sign of every term in the expression which is being subtracted and adding this result to the other expression.

Multiplication of binomials, the FOIL method.

The FOIL method is a way to multiply binomials. "FOIL" is an acronym to remember a set of rules to perform this multiplication. To FOIL you multiply together all of the following:
  • F: First terms
  • O: Outer terms
  • I: Inner terms
  • L: Last terms
and write them as a polynomial.

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Special products
The following are some of the products which occurs frequently in mathematics:

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