ALGEBRA

INTRODUCTIONAlgebraic expression – a group of numbers, symbols, and variables that express an operation or a series of operations.

EXAMPLES: a-8 b-2 z+12 etc……

DEFINITIONS

Variable – A variable is a letter or symbol that represents a number. It is an unknown quantity

EXAMPLES: 5+z=13 4-y=1 etc……

Evaluating an algebraic expression – To find the value of an algebraic expression we can substitute numbers for variables.

Examples: m+7,m-3 etc…(‘m’ variable can be any number) m + 8 if m = 2 then 2 + 8 = 10 z – 6 if z = 10 then 10 - 6 = 4

Like and unlike termsLike terms:

like terms are terms that have the same variables and powers

Example: 8xyz2 and 5xyz2 are like terms because they have the same variables and power

unlike terms:

Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. Example: 3abc and 3ghi are unlike terms because they have different variables

Difference between like and unlike terms

1.Like terms can be added together to simplify an expression.2.When adding like terms, add the numerical coefficients and retain the variable.3.Unlike terms cannot be added together since the variables represent different items.

Words That Lead to Addition

Sum More than Increased Plus Altogether

Words That Lead to Subtraction

Decreased Less Difference Minus How many more

Terms and coefficientsTerms: Terms are the elements separated by the plus or minus signs.

Example: 3x2+2y+7xy+5 This example has four terms, 3x2, 2y, 7xy, and 5.

Coefficients:A number used to multiply a variable.

Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.

Monomials,binomials,trinomials and

polynomials

Monomial:An expression with one term is called a monomial

Binomial:An expression with two terms is called a binomial

Trinomial:An expression with three terms is called a trinomial

Polynomial:A polynomial is an expression consisting of variables and coefficients more than three terms.

Examples:

,

Identity

1. An identity is an equality, which is true for all values of the variables in the equality2. An equation is not an identity.

Standard identities

1) (a+b) 2 = a2 + 2ab + b 2

2) (a-b) 2 = a2-2ab + b2

3) (a+b) (a-b) = a2- b 2 4) (x+a)(x+b)=x 2 +(a+b)x+ab

We can also write Algebraic Expressionsfor These Word Phrases

Ten more than a number n+10A number decrease by 5 w-56 less than a number z-6A number increased by 8 n+8The sum of a number & 9 n+94 more than a number y+4

A number s plus 2 s+2A number decrease by 1 k-131 less than a number x-31A number b increased by 7 b=7The sum of a number & 6 n=69 more than a number z=9

Prepared by G.SRI HARSHA VIII D