Addition and Subtraction of Algebraic Expressions

While adding or subtracting,

We add subtract like terms

Add 3 𝑥 & 4𝑥

 3𝑥 + 4𝑥

= 𝑥 (3 + 4)

= x × 7

= 7𝑥 

Add 8xy & 2𝑥

8𝑥y + 2𝑥  

Since 8𝑥y & 2𝑥 are unlike terms

We cannot add them

Add 8𝑥y, 4𝑥y & 2𝑥y

8𝑥y + 4𝑥y + 2xy

= xy (8 + 4 + 2)

= xy (14)

= 14𝑥y     

Subtract 4n from 7n

7n − 4n

= n(7 − 4)

= n × 3

= 3n

Subtract 5ab from 11ab

11ab − 5ab

= ab (11 − 5)

= ab × 6

= 6ab

Now,

Suppose our expressions are bigger

Add 3x + 11 & 7x − 5

(3𝑥 + 11) + (7𝑥 – 5)

We group like terms together

= (3x + 7x) + (11 − 5)

 = 10𝑥 + 6

Add (3x + 11 + 8z) & 7x − 5

(3𝑥 + 11 + 8z) + (7x − 5)

= (3x + 7x) + (11 − 5 ) + 8z

= x (3 + 7) + (6) + 8z

= 10x + 6 + 8z

= 10x + 8z + 6   

  Subtract (a − b) from 3a − b + 4

(3a − b + 4) − (a − b)

= 3a − b + 4 − a + b

= (3a − a) + (−b + b) + 4

= (3a − a ) + (b − b) + 4

= 2a  + 0 + 4

= 2a + 4