In subtraction of like terms when all the terms are negative, subtract their coefficients, also the variables and power of the like terms remains the same.
For example:
1. Subtract xy from 10xy.
Here, 10xy, xy are like terms
The difference of the coefficients = 10  1, [xy means 1xy]
Therefore, 10xy  xy = 9xy
Note: The result of subtraction of two like terms is also a like terms whose numerical coefficient is obtained by taking the difference of the numerical coefficients of like terms.
2. Subtract 4x from 8x
Here, 4x and 8x are like terms.
= 8x – (4x)
= 8x  4x, [open the parenthesis]
= 12x.
3. Subtract 3x from 7x
Here, 3x and 7x are like terms
= 7x – (3x)
= 7x + 3x, [since negative times negative is positive so, (3x) = +3x]
= 4x.
4. 15x  4x  12y  3y
Here, 15x and 4x are like terms
and also 12y and 3y are like terms
15x  4x = 11x
12y  3y = 9y
Therefore, the answer is 11x  9y.
5. Subtract 4x + 3y + z from 2x + 3y  z.
(2x + 3y  z)  (4x + 3y + z)
= 2x + 3y  z  4x  3y  z, [open the parenthesis]
Here, 4x and 2x are like terms,
3y and 3y are like terms
and also z and z are like terms.
Now arranging the like terms, we get
= 2x  4x + 3y  3y  z  z
= 2x + 0  2z, [Since, + 3y  3y = 0]
= 2x  2z
Note: The subtraction of two or more like terms is another like term whose numerical coefficient is the subtraction of the numerical coefficients of these like terms.
Thus, we observed that for solving the problems on subtracting like terms we can follow the same rules, as those used for solving subtraction of integers.
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Adding and Subtracting Like Terms
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