In mathematics, with reference to Polynomials, the word monomial can have one of two different meanings:

1. It is product of variables or any value obtained by many multiplications of a variable (we can call it as power of a variable), if the variable is “x”, then the monomial can be either “x” or  “xn”.

Example: a, b5

2. Monomial can also be product of a non zero number and a variable.

Example:  4x, 5ab2  , -2xy3z2

Monomials are essentially an algebraic expression consisting only one term. The term (fixed number) along with the variable is called as its Coefficient. The degree of the monomial is the sum of the exponents of the included variables.

Degree of 3x is 1.
Degree of 5x2y will be 3 as degree of x2 is 2 and that of y is 1.

Monomials can be added or subtracted only if they are like terms. Addition or subtraction of monomials is done by combining like terms.
• 2 + 5x + 12x
Here like terms are 5x and 12 x , so we add them by combining.
2 + 5x + 12x = 2 + x(5 + 12)
= 2 + 17 x.

• Add 12x and 6xy
Since the terms are not like terms we get the addition as
12x + 6xy.

•  Add -3 x2y   and 2xy2:
Here even though both the terms have same variables and equal
degree they can not be considered as like terms.

More Examples:
1) -9c + 4c2 + 4c
combine like terms together.

= 4c2 - 9c + 4c
= 4c2 + c(-9 + 4)
= 4c2  - 5c

2) -3m3 - 7m3  + 10 m3

= m3 (- 3 - 7 + 10)
= 0m3  = 0

3) 32 + 7n2 + 18 n2

Combine like terms

= 32 + n2 (7+18)
= 32 + 25 n2

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