In algebra the definition given to a monomial and a polynomial is that a monomial is a product of positive integer powers of similar or different variables. It has only one term and does not contain a variable in its denominator. A polynomial is the sum of one or more like or unlike terms. Polynomials are generally written in descending order and they are in their simplest form when they contain no like terms.
Distributive property also known as distributive law is basically breaking down numbers; separating like and unlike terms thus putting like terms together as well as unlike terms together. Property of distribution makes working with numbers and values much easier. It also helps with mental sums and is recommended for kids. Distributive property is used to multiply a monomial by a polynomial by expanding the products of both or even divide a polynomial by a monomial. It’s also used to get rid of parentheses.
The big question is whether the distributive property is always used when multiplying monomials and polynomials. The answer is a resounding yes because polynomials are sums of monomials thus if you are to multiply several polynomials it would be easier to first distribute them so as to be able to do the calculation more easily and accurately (Rich, 2010, p. 62). However, when all values are monomials the property of distribution is unnecessary.
Distribution of property is important in situations such as dividing a polynomial by a monomial where each term has to be divided by the monomial (Rich, 2010, p. 17). When multiplying a monomial by a polynomial which requires expanding the products of the polynomial and monomial. When finding the product of monomials and finally distribution of property is used in getting rid of parentheses.
Rich, B. (2010). Schaum’s Easy Outline of Elementary Algebra, 2nd Edition. London: Mc-Graw