Published By-

Param Publication

Addition or subtraction of like terms
     The sum or difference of several like terms is another like term whose coefficient is the sum or difference of those like terms.
    Illustration 1 
        Add the following : 3xy, 10xy and 5xy.
    Solution
        The sum of the numerical coefficients of the given like terms is 3 + 10 + 5 = 18.
        Hence, 3xy + 10xy + 5xy = 18xy.

    Illustration  2
         Add the following : – 2p2q,  – 9p2q,  – 14p2q and  – 5p2q.
    Solution
        The sum of the numerical coefficients (without negative sign) is : 2 + 9 + 14 + 5 = 30
        Hence, –2p2q – 9p2q – 14p2q – 5p2q = – 30p2q.
 
    Illustration  3
         Add the following : 3x + y + 4 and 4x + 3y + 7.
    Solution    
        Horizontal Method
            (3x + y + 4) + (4x + 3y + 7)
        =     (3x + 4x) + (y + 3y) + (4 + 7)
        =     (3 + 4)x + (1 + 3)y + (4 + 7)
        =     7x + 4y + 11

                 Or

      

Illustration 4
         Add the following : 3x + 4y + 5z and 2x – 3y – 4z.
 Solution
        Horizontal Method
            (3x + 4y + 5z) + (2x – 3y – 4z)
        =     (3x + 2x) + (4y – 3y) + (5z – 4z)
        =     (3 + 2)x + (4 – 3)y + (5 – 4)z
        =     5x + y + z

                 Or

   

NOTE : To subtract an expression from another, we change the sign (from' + ' to ' – ' and from' – ' to ' + ') of each term of the expression to be subtracted and then add the two expressions.


Illustration 5 
        Subtract :
         (i) 3p from 7p        (ii) – 8x from 9x    (iii) – 3a from 7a    (iv) – 9b from – 2b
 Solution
        (i)     7p – 3p = (7 – 3)p = 4p
        (ii)     9x – (–8x) = 9x + 8x =(9 + 8) x = 17x
        (iii)     7a – (–3a) = 7a + 3a = (7 + 3)a = 10a
        (iv)     – 2b – (– 9b) = – 2b + 9b = (– 2 + 9)b = 7b

Illustration 6 
        What should be subtracted from 2p3 – 4p2 + 5p – 6 to obtain p2 – 2p + 1 ?
 Solution
        Let X denote the required expression. 
        Then, (2p3 – 4p2 + 5p – 6) – X = p2 – 2p + 1    
        Hence, required expression          
        X = (2p3 – 4p2 + 5p – 6) – (p2 – 2p + 1)
        X = 2p3 – 4p2 + 5p – 6 – p2 + 2p – 1
        X = 2p3 – 4p2 – p2 + 5p + 2p – 7
        X = 2p3 – 5p2 + 7p – 7

NOTE : When a grouping symbol preceded by, ‘–' sign is removed or inserted, then the sign of each term of the corresponding expression is changed (from '+' to '–' and from '–'  to  '+'). 

Illustration 7 
        Simplify : 2x – {4y – (3x – 5y)}.
 Solution
        We first remove the innermost grouping symbol ( ) and then braces { }.
        Thus, we have
            2x – {4y – (3x – 5y)}
            = 2x – {4y – 3x + 5y}        [Removing ( )]
            = 2x – {9y – 3x} 
            = 2x – 9y + 3x
            = 2x + 3x – 9y
            = 5x – 9y.

Illustration 8
        Simplify and find the value of the following expression when a = 2 and b = 3 :
        4(a2 + b2 + 2ab) – [4(a2 + b2 – 2ab) – {– b3 + 4(a – 3)}]    
  Solution
        Proceeding outward from the innermost bracket,
        4(a2 + b2 + 2ab) – [4(a2 + b2 – 2ab) – {– b3 + 4(a – 3)}]
            = 4(a2 + b2 + 2ab) – [4(a2 + b2 – 2ab) – {– b3 + 4a – 12}]
            = 4a2 + 4b2 + 8ab – [4a2 + 4b2 – 8ab + b3 – 4a + 12]
            = 4a2 + 4b2 + 8ab – 4a2 – 4b2 + 8ab – b3 + 4a – 12
            = 4a2 – 4a2 + 4b2 – 4b2 + 8ab + 8ab – b3 + 4a – 12
            =  (4 – 4)a2 + (4 – 4)b2 + (8 + 8)ab – b3 + 4a – 12
            = 16ab – b3 +  4a – 12
        Thus va    lue of this expression for a = 2 and b = 3 is :
            16 × 2 × 3 – (3)3 + 4 × 2 – 12  = 96 – 27 + 8 – 12 = 65.

 

EDUCARE

Course : CBSE Class 7

Start Date : 26.01.2022

End Date : 03.03.2022

Types of Batch : Live Online Class

Subject M T W T F S S
Mathematics(120 hours) 7:00 PM 7:00 PM 7:00 PM 7:00 PM 7:00 PM - -
Class 7 - ALL Subjects
veda skill training academy

Course : CBSE Class 7

Start Date : 27.01.2022

End Date : 31.03.2022

Types of Batch : Live Online Class

Subject M T W T F S S
Mathematics(30 hours) 6:00 AM 6:00 AM 6:00 AM 6:00 AM 6:00 AM 12:45 PM 12:45 PM
Science(30 hours) 6:00 AM 6:00 AM 6:00 AM 6:00 AM 6:00 AM 6:00 AM 12:45 PM