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, 5a
2b
2 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 :- 2p
2 + 8q
2 + 3r
2 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)
=14a
2b
2c
2 + 21ab
2c
2 + 56a
2bc
2 Q4. Multiply (15mn+12m) and (3mn+8n)
(15mn+12m)(3mn+8n)
15mn (3mn+8n)+12m (3mn+8n)
=45m
2n
2 + 120mn
2 + 36m
2n + 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)