Like terms are the mathematical terms with the same bases and same exponents.
The process of adding/subtracting the like terms is mostly used while doing the operations on polynomials.
Example:
2x and 3x are like terms.
x^3 and 2x^3 are like terms.
x^2 and x^2y^2 are not like terms because the second term is including y also which is not there in the first term.
Adding or Subtracting Like Terms:
While adding or subtracting the like terms, we operate on the coefficients keeping the variable base and powers same.
Usually we need to add/subtract the like terms while operating with the polynomials.
Example 1:
Simplify 3x + 2x.
Solution:
Here 3x and 2x are like terms because they have same base(x).
While adding we need to consider only the coefficients and so we get 3+2 = 5 for the base is x.
So 3x+2x = 5x.
Example 2 :
Simplify 2×2 + 4×2.
Solution:
Here 2×2 and 4×2 are like terms because they have same base(x) and the same power(2).
While adding we need to consider only the coefficients and so we get 2+4 = 6 for the term x^2.
So, 2×2 + 4×2 = 6×2.
Example 3:
Simplify 3x + 5 -2x.
Solution:
Here 3x and 2x are like terms because they have same base(x).
So, we write 3x + 5 -2x = (3x-2x)+5
While adding we need to consider only the coefficients and so we get 3-2 = 1 for the base x.
So, 3x+5 – 2x = 1x + 5 = x+5.
Example 4:
Simplify 4x + 6 + x -8.
Solution:
Here 4x and x are like terms because they have same base(x).
Here 6 and -8 are like terms because they both are constants.
So, we can write 4x + 6 + x -8 = (4x+x) + (6-8)
While adding we need to consider only the coefficients and so we get
4+1 = 5 and 6-8 = -2.
So, 4x + 6 + x -8 = (4x+x) + (6-8) = 5x -2.
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