Algebra

1. A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
2. A set together with a pair of binary operations defined on the set. Usually, the set and the operations include an identity element, and the operations are commutative or associative.

[Middle English, bone-setting, and Italian, algebra, both from Medieval Latin, from Arabic al-jabr (wa-l-muqābala), the restoration (and the compensation), addition (and subtraction) : al-, the + jabr, bone-setting, restoration (from jabara, to set (bones), force, restore).

Words that describe mathematical expression 

In order to solve world problems or real world problems you need to know the key words to translate a verbal expression(phrase) into algebraic expression.
Sometimes, you find yourself having to write out your own algebraic expression based on the wording of a problem. 
In that situation, you want to 

1. read the problem carefully,
2. pick out key words and phrases and determine their equivalent mathematical meaning,
3. replace any unknowns with a symbol, and
4. put it all together in an algebraic expression                                                                                                                                                       The first step in solving a word problem is always to read the problem. You need to be able to translate words into mathematical symbols, focusing on keywords that indicate the mathematical procedures required to solve the problem—both the operation and the order of the expression. In much the same way that you can translate Spanish into English, you can translate English words into symbols, the language of mathematics. Many (if not all) keywords that indicate mathematical operations are familiar words                                                                                                                            for example   the sum of 5 and a number                                          means 5+x     sum is a key word representing '+ ' and  for unknown number we used  a symbol 'x'.                                                                                                                                                                 Write the phrase as an algebraic expression. The product of 5 and a number.
   
    

   Again, we want to rewrite this as an algebraic expression, not evaluate it. This time, the phrase that correlates with our operation is 'product' - so what operation will we be doing this time?   If you said multiplication, you are right on. Again, we have the phrase 'a number', which again is going to be replaced with an unknown x, since we do not know what the number is.   Let’s see what we get for this answer:

   
    

   The product of 5 and a number

   *'product' = multiplication *'a number' = unknown x

                                                                                                                                                           We have a number of key words which describe mathematical operations but in this presentation you will find some key words which are commonly used and these words  can help u in translating  algebraic expressions.   
5.  Some more Key words                                                                                                                                                          following are some key words and phrases that translate into an equal sign (=):
    

   Equal Sign (=) :  equals, gives, is, yields, amounts to, is the same as

   some key words that represent a power to a base .                                                                        Exponent ,squared,cube ,power                                                                                        
   For example three times a number having exponent 2  means  3X²