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What are Algebraic expressions?
Algebraic expressions are formed by terms which contain both variables and constants. A term is a constant or a product of two or more constants and variables.
Eg:-  4x+5, 5y-9, 6p+35, etc.

Monomials, Binomials  and Polynomials
An Algrebraic expression is said to be a monomial if it contains only one term. Ex :- 8axyz, 5a²b²
An Algrebraic expression is said to be a bionomial if it contains two unlike terms. Ex :-  ax + b, 30a + b 
An Algrebraic expression is said to be a trinomial if it contains three unlike terms. Ex :-   2p² + 8q² + 3r²

Addition of Algebraic Expressions
Addition of two algebraic expression can be done in this way
Q1. Add 6ax+11by+17cz+15 and 8ax-8cz+13

        6ax+11by+17cz+15
        8ax             -8cz+13
       14ax+11by+9cz+28

Subtraction of Algebraic Expressions
Subraction of two algebraic expression can be done in this way
Q2. Subtract 12x+7y-15z from 17x+8y-15z

       17x+8y-15z
       12x+7y-15z
       (-)   (-)  (+)
        5x + y

Multiplication of Algebraic Expressions
Multiplication of two algebraic expression can be done in this way
Q3.  Multiply (2ab+3bc+8ca) by 7abc

         7abc (2ab+3bc+8ca)
      = 7abc(2ab)+7abc(3bc) + 7abc (8ca)
      =14a²b²c² + 21ab²c² + 56a²bc²

Q4.  Multiply (15mn+12m) and (3mn+8n)

         (15mn+12m)(3mn+8n)
         15mn (3mn+8n)+12m (3mn+8n)
        =45m²n² + 120mn² + 36m²n + 96mn

Standard Indentities 

Indentity I -  (a + b)² = a² + 2ab + b² 
Indentity II -  (a - b)² = a² - 2ab + b² 
Indentity III -  a² - b² = (a- b) (a +b)