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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
= -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.
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