Adding and subtracting like terms is the same as adding and subtracting of numbers, i.e., natural numbers, whole numbers and integers.

So, the sum and the difference of several like terms is another like term whose coefficient is the sum and the difference of the coefficient of several like terms.

Examples of adding like terms:

**1.** Add 7mn, -9mn, -8mn

The sum will be another like term with coefficient 7 + (-9) + (-8) = -10

Therefore, 7mn + (-9mn) + (-8mn) = -10mn

**2.** Sum of 5xyz, -7xyz, -9xyz and 10xyz

The sum will be another like term with coefficient 5 + (-7) + (-9) + (10) = -1

Therefore, 5xyz + (-7xyz) + (-9xyz) + 10xyz = -1xyz

Examples
of subtracting like terms:

**1.** Subtract 12xy
from 27xy

The difference will be another like term with coefficient 27 – 12 = 15

Therefore, 27xy – 12xy = 15xy

**2.** Difference of 15ab
from 7ab

The difference will be another like term with coefficient 7 – 15 = -8

Therefore, 7ab – 15ab = -8ab

Examples of combining addition and subtraction of like terms:

**1. **Combine the
like terms and then simplify 7a – 3b + 4ab + 9b – 6ab – 3a

= 7a – 3a – 3b + 9b + 4ab – 6ab → arrange the like terms

= (7 - 3)a + (-3 + 9)b + (4 - 6)ab → combine like terms

= (4)a + (6)b + (-2)ab → simplify

= 4a + 6b - 2ab

= -5z

= (-5 – 4)z

= (-9)z

= -9z

While adding and subtracting like terms we collect different groups of like terms, then we find the sum and the difference of like terms in each group.

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Adding and Subtracting Like Terms

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