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.
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]
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]
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.