GRE Algebra | Operations with Algebraic Expressions

An expression contain variables, numbers and operation symbols is called an algebraic expression.Every expression can be written as a single term or sum of terms.
Here are some examples of algebraic expressions.

(1): 5x + 2y + 7 
(2): 2x2 + 3y2 + 5
(3): x3z + 2x2 + 3x + 9
(4): 4x/(2x + 1) 

A number multiplied by the variables is called coefficient of a term.
In above example (2), 2 is coefficient of 2x2 and 3 is the coefficient of 3y2 and 5 is the constant.

Operations performed on algebraic expression are:

  1. Addition & Subtraction:
    On performing addition or subtraction on algebraic expression the coefficients of same degree added or subtracted.
    For example:

    => 3x + 4x = 7x
    => a3 + 4a2 - 3a2 + 2 = a3 + a2 + 2 
  2. Multiplication:
    Two algebraic expressions can be multiplied by multiplying each term of first expression to the each term of the second expression.
    For example:



    => (3a + 3)(2a - 8) = 3a(2a) + 3a(-8) + 3(2a) - 3(8)
                        = 6a2 - 24a + 6a - 24
                        = 6a2 - 18a - 24  
  3. Common Factor:
    A number or variable can be factored out of each term of expression if it is common in all the terms.
    For example:

    => 3y + 15 = 3(y + 5)
    => 9x2 - 3x = 3x(3x - 1)
    => 4y2 + 8y/ 2y+ 4 = 4y(y + 2)/ 2(y+2) =  4y/2 (where y ≠ 2 ) 
  4. Identity:
    It can be defined as a statement of equality between two algebraic expression and it is true for all possible values.
    For example:

    (x + y)2 = x2 + 2xy + y2
    (x - y)2 = x2 - 2xy + y2
    (x + y)3 = x3 + 3x2y + 3xy2 + y3
    (x - y)3 = x3 - 3x2y + 3xy2 - y3
    x2 - y2 = (x + y)(x - y)
    x3 - y3 = (x - y)(x2 + xy + y2) 
    x3 + y3 = (x + y)(x2 - xy + y2) 
    x2 + y2 + z2 = (x + y + z)2 - 2(xy + yz + zx)
    x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)
    (x + y)(y + z)(z + x) = (x + y + z)(xy + yz + zx) - xyz 

An equation is true only for certain values of variables.

  1. Linear equation in one variable:
    2a + 4 = 8 
  2. Linear equation in two variables:
    5a + 7b = 49 
  3. A quadratic equation in one variable:
    4a2 + 2a = 16 


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.




Article Tags :

Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.