POLYNOMIAL
An algebraic expression which consists of two or more terms is called a polynomial.
For example, a + b, x^{3}  y^{3} , x^{2} + x y + y^{2}.
1) A polynomial which consists of exactly two terms is a binomial.
For example 2 x^{2} + x, x^{2} + y^{2}.
2) A polynomial which consists of exactly three terms is a trinomial.
For example, x^{2} + 3 x + 2, a^{2} + a b + b^{2}
etc. Usually a polynomial is
written either in the ascending or descending powers of the variable,
say x. This form of a polynomial
is called a standard form. For example x^{4}
+ 3 x^{3} + x^{2}
+ 7x + 5 and 2 + 3 y + 7 y^{2}
 y^{3} are polynomials in the standard form. Descending
order is used more commonly.
Addition:
In order to add given polynomials, we adopt two steps.
1) Arrange the given polynomials, such that like terms are in one column.
2) Add the coefficients of each column separately.
Subtraction :
This is done in two steps :
1) Arrange the given polynomials, such that like terms are in one column.
2) Change the signs of the terms of the polynomial and then add.
Example Add 4 a  3 b,  2 a + b, 5 a  3 b and  6
a + 4 b
Solution: The required sum
=( 4 a  3 b ) + (  2 a + b ) + ( 5 a  3 b ) + ( 6 a + 4 b )
= ( 4 a  2 a + 5 a  6 a ) + (  3 b + b  3 b + 4 b )
= ( 9 a  8 a ) + ( 5 b  6 b )
= a + (  b )
= a  b
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