Chap 9 ALGEBRAIC EXPRESSIONS AND IDENTITIES

Chap 9

ALGEBRAIC EXPRESSIONS AND IDENTITIES

SOME IMPORTANT FACTS

1.      A combination of constants and variables connected by + , - , x , ÷ is called  an algebraic expression.

2.      The several parts of the expression separated by  + or – sign are called terms.

3.      A monomial is a one term expression which is either a constant or the product of constant and one or more variable with positive integral exponents.

4.      A Binomial contains two terms .

5.      A trinomial contains three terms.

6.      The terms having same literal factors are called like terms, otherwise they are called unlike terms.

7.      The sum or difference of several like terms is another like term whose coefficient is the sum or difference of those like terms.

8.      In adding or subtracting algebraic expressions, we collect different groups of like terms and find the sum or difference of like terms in each group.

9.      If x is any variable and a , b are positive integers, then ;

x ^a x ^b = x ^{(a + b)}

x ^a y ^a = (xy) ^a

(x ^a) ^b = x ^(ab)

x ^(a/b) = b^th root of (x ^a) = ( b^th  (x) ) ^a

x ^(-a) = 1 / x ^a

x ^{(a - b)} = x ^a / x ^b

10.  If P ,Q , R are three monomials, then

P x ( Q ± R ) = ( P x Q ) ± ( P x R )

( Q ± R ) x P  = ( Q x P ) ± ( R x P )

11.  ( a + b ) x ( c + d )  =  a x ( c + d ) + b x ( c + d ) = ac + ad + bc + bd.

12.  Some identities are :

a)     (a+b)² = a² + 2ab + b²

b)    ( a – b )² =  a² - 2ab + b²

c)     ( a+ b )( a + b ) = a² -  b²

d)    ( x + a )( x + b )  = x²  + ( a + b ) x + ab