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One monomial is an algebraic term formed by a number, a variable, or by a multiplication between numbers and variables.
The numerical part of the monomial is called the coefficient and the part composed of variables is called the literal part. For example, in the monomial 2xy the coefficient is 2 and the literal part is xy.
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See below how to algebraic calculation involving monomials.
A addition or subtraction of monomials is made only between monomials that have the same literal part. When they are, we add or subtract the coefficients and keep the literal part.
Example:
Perform addition and subtraction operations between monomials.
The)
The literal part of all three monomials is , then we perform the operations between the coefficients and keep the literal part:
B)
Not all terms have the same literal part, so we perform operations only between the coefficients of those that do:
Amultiplication of monomials is done by multiplying the coefficients and multiplying the literal parts, whether they are equal or not.
However, if the literal parts are powers with the same base, we use the following property of potentiation: .
Example:
Multiply between monomials.
The)
We multiply the coefficients:
We multiply the literal parts:
Therefore:
B)
We multiply the coefficients:
We multiply the literal parts:
Therefore:
At division of monomials, we must divide between the coefficients and between the literal parts of the same base, using another power property: .
Variables that appear in only one term of the division are retained.
Example:
Carry out divisions between monomials.
The)
We divide the coefficients:
We split the literal parts
Note that the variable b is retained as it only appears in the second term.
Therefore:
B)
We divide the coefficients:
We split the literal parts:
Note that the variable b is retained as it only appears in the first term.
Therefore:
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