Add and Subtract Polynomials

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Definition: - An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial.
 

Examples: -
• 5x^3 – 4x^2 + 6x -3 is a polynomial in one variable x.
• 9y^4 +6 y^3 + 10y^2 -8y +2/5 is a polynomial in one variable y.
• 3 +2x^2 -6x^2y +5xy^2 is a polynomial in two variable x and y.
• 5+ 8x^ (3/2) +4x^2 is an expression but not a polynomial, since it contains a term containing x^ (3/2), where 3/2 is         not a non-negative integer.
 

Note: - A polynomial containing one term only, consisting of a constant is called a constant polynomial.
 
Example: - 3, -5, 7/8 etc. are all constant polynomial.
In general, every real number is a constant polynomial.
 
A polynomial consisting of one term, namely zero only is called a zero polynomial.

Example1: - Add and subtract the following polynomials
                   2x^2 + 5x + 9 and 6x^2 + 8x + 3
 
Solution: -
             (2x^2 + 5x + 9) + (6x^2 + 8x + 3) = (2x^2 + 6x^2) + (5x+8x) + (9+3)
                                                                        = 8x^2 + 13x + 12
 
             (2x^2 + 5x + 9) – (6x^2 + 8x + 3) = 2x^2 + 5x + 9 - 6x^2 - 8x – 3
                                                                        = (2x^2 – 6x^2) + (5x – 8x) + (9 – 3)
                                                                        = -4x^2 – 3x + 6
 

Example2: - Add and subtract the polynomials
                     2x + y – 3 and 3x + 2y – 8
 
Solution: -
             (2x + y – 3) + (3x + 2y – 8) = 2x+y –3+3x+2y–8
                                                             = 5x+3y-11
 
            (2x + y – 3) - (3x + 2y – 8) = 2x+y–3-3x-2y+8
                                                            = -x-y+5

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