How to add/subtract terms which contain variable/variables
Only Like-terms in an expression can be added or subtracted.Â
Constant like-terms are added/subtracted same as we do addition/subtraction of integers.Â
To add/ subtract like-terms containing variable/variables, we add/subtract their coefficients and write the variable/variables beside it.Â
Let us understand this with following examples.
Example 1:
Simplify: 2p + 3p
Solution:Â
This expression has two terms, 2p and 3p.
In 2p, 2 is coefficient and p is variable.
In 3p, 3 is coefficient and p is variable.Â
(Both have same variable. So, we say 2p and 3p are like-terms.)
To add 2p and 3p, we add the coefficients 2 and 3 and write p beside it. That is:
2p + 3p = (2 + 3) p = 5p
Thus, the expression 2p + 3p simplified to 5p.
Example 2:
Simplify: k - 3k
Solution:Â
This expression also has two terms, k and -3k.
In k, 1 is coefficient and k is variable.
In -3k, -3 is coefficient and k is variable.Â
(So, k and -3k are like-terms.)
Thus:
k - 3k = (1 - 3) k = - 2k
Expression k - 3k simplified to - 2k.
Example 3:
Simplify: t + 5 - 8t - 4 - 2t
Solution:Â
This expression has five terms, t , 5 , - 8t , - 4 and - 2t
Among these,
 t, - 8t and - 2t are like-terms.
5 and - 4 are also like-terms.
t + 5 - 8t - 4 - 2tÂ
= t - 8t - 2t + 5 - 4Â Â Â (Gathered like-terms)Â Â Â Â Â Â
= (1 - 8 - 2) t + 1
= - 9t + 1
Thus, t + 5 - 8t - 4 - 2t simplified to - 9t +1.
Example 4:
Simplify: y² + 3y - 4x - y² - 8x + 5
Solution:Â
This expression has six terms, y² , 3y , - 4x , - y² , - 8x and 5
Among these,
y² and - y² are like-terms.
- 4x and - 8x are like-terms
3y and 5 do not have any like-term.
y² + 3y - 4x - y² - 8x + 5Â
= y² - y² - 4x - 8x + 3y + 5  (Gathered like-terms)
                             Â
= (1 - 1) y² + (- 4 - 8)x + 3y + 5
= - 12x + 3y + 5          (As 0y² = 0 × y² = 0)
 Thus, y² + 3y - 4x - y² - 8x + 5 simplified to - 12x + 3y + 5
Example 5:
Can the following expression be simplified?
xy² + 4y - 2x - x²y + 5
Solution:Â
This expression has five terms, xy² , 4y , - 2x , - x²y and 5
None of these terms are like-terms. So, this expression cannot be simplified.
Remember: We cannot add/subtract the terms which are not like-terms. For exampleÂ
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