Eight Standard >> Operations on algebraic expressions | Addition and subtraction operation

Algebraic Expressions: Addition & Subtraction

2+5x ≠ 7x
     [because they are not like turms]
\(2x+5x=(2+5)x=7x\)
      [because they are like turms]

Ex 1: Add these numbers 3xy, -5xy, 7yx

Sum=\(3xy-5xy+7yx\)
     =\((3-5+7)xy\)
     =\(5xy\)

Ex 2: Sum of 7x+3y, 8x, 3x-5y
The sum=7x+3y+8x+3x-5y   
             =(7+8+3)x+(3-5)y                                               

              =18x - 2y   Ans.

Ex 3: \(5x^{2} -\frac{1}{3}x+\frac{5}{2}\)   and \(2x^{2} -\frac{2}{3}x+\frac{3}{2}\) 

Solution:
 The sum=\(5x^{2} -\frac{1}{3}x+\frac{5}{2}+2x^{2} -\frac{2}{3}x+\frac{3}{2}\)  
         =\( (5+2)x^{2}+( -\frac{1}{3}-\frac{2}{3})x+\frac{5}{2}+\frac{3}{2}\) 
         =\( 7x^{2}+(\frac{-1-2}{3})x+\frac{5+3}{2}\)
         =\( 7x^{2}-(\frac{3}{3})x+\frac{8}{2}\)  
         =\( 7x^{2}-x+4\) Ans.

 Subtract: In order to subtract change the sign of algebric expression which is to be substracted and then added.

Ex 1: Subtract a-b from a+b

Solution: 
Difference=(a+b)-(a-b)
              =a+b-a+b
              =2b Ans.

Ex 2: Subtract \(5a^{2}-2ab+b^{2}\) from \(3a^{2}-b^{2}\)

Solution: 
Difference=\(3a^{2}-b^{2}\)-\(5a^{2}-2ab+b^{2}\)
              =\(3a^{2}-b^{2}-5a^{2}+2ab-b^{2}\)
              =\((3-5)a^{2}+(-1-1)b^{2}+2ab\)
              =\(-2a^{2}-2b^{2}+2ab\) Ans.