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.