3.
Positive Like terms :
To add several positive like terms, we proceed as follows :
Step 1 : Obtain all like terms.
Step 2 : Find the sum of the numerical coefficients of all terms.
Step 3 : Write the required sum as a like term whose numerical coefficient
is the numerical obtained in Step 2 and literal factor is same as the literal
factors of the given like terms.
Example:
1) Add 4xy, 12xy and 3xy.
Solution :
4xy ---> coefficient 4
12xy ----> coefficient 12
3xy -----> coefficient 3
Add all the coefficients ( 4 + 12 + 3 = 19).
Hence, 4xy + 12xy + 3xy = 19xy.
ADDITION OF ALGEBRAIC EXPRESSIONS
4. ADDITION OF ALGEBRAIC EXPRESSIONS
Addition of Negative Like terms
To add negative like terms, we proceed as follows :
Step 1 : Obtain all like terms.
Step 2 : Find the sum of the negative numerical coefficients of all terms.
Step 3 : Write an expression with numerical coefficients obtain in Step 2
and literal coefficients with negative sign in the beginning.
Example:
1) Add -7xy, -3xy and -9xy.
Solution :
-7xy ----> coefficient -7
-3xy ----> coefficient -3
-9xy ----> coefficient -9
Add all the coefficients ( -7-3-9 = -19)
Hence,-7xy -3xy -9xy = -19xy
2) Add -4ab, -7ab,-10ab and -3ay
5. ADDITION OF ALGEBRAIC EXPRESSIONS
Addition of Algebraic Expressions with Like and Unlike terms
In adding algebraic expressions containing like and unlike terms, we collect
different groups of like terms and find the sum of like terms in each group
bye the methods discussed above.
Example:
Add the following :
1) 7x +4 and 3x -1
= (7x + 4) + (3x -1)
= 7x + 4 + 3x -1 [ Marking of like terms]
= 10x + 3
2) a2 + b2 + c2 – 3abc and a2 – b2 + c2 + abc
= (a2 + b2 + c2 – 3abc) + (a2 – b2 + c2 + abc)
= a2 + b2 + c2 – 3abc + a2 – b2 + c2 + abc
= a2 + b2 + c2 - 3abc + a2 -b2 + c2 + abc [ Marking of like terms]
= 2a2 + 0 + 2c2 - 2abc
= 2a2 + 2c2 - 2abc
