Adding and Subtracting Like Terms

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  


2. Combine the like terms and simplify -5z5 + 2 – 3z3 + 8z + 7z3 – 4z5 – z.

= -5z5 – 4z5 – 3z3 + 7z3 + 8z – z + 2              arrange the like terms.

= (-5 – 4)z5 + (-3 + 7)z3 + (8 - 1)z + 2           combine like terms.

= (-9)z5 + (4)z3 + (7)z + 2                            simplify.

= -9z5 + 4z3 + 7z + 2

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.

Terms

Like and Unlike Terms

Like Terms

Addition of Like Terms

Subtraction of Like Terms

Adding and Subtracting Like Terms

Unlike Terms

Addition of Unlike Terms

Subtraction of Unlike Terms






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