MAT 117 /MAT117 Week 1 Discussion Question
Week 1 DQ 2
1. Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not.
2. In what situations would distribution become important?
3. Provide an example using the distributive property for your classmates to solve or evaluate.
A monomial is a number, a variable, or a product of numbers and variables raised to natural number powers... Monomials do not contain division by variables. Also, if an expression contains addition or subtraction signs, it is not a monomial.
Polynomials are the sum of two or more monomials.
Distribution property is used frequently when multiplying monomials and polynomials. It is not always required however. If there is not a variable before parentheses, it is not needed. x(7-2) would required distributing x to both terms in the parentheses. 7-2 however does not require distribution.
An example of an equation requiring distribution is:
2(3^3) - (6/2)^3
After reading the text, I learned that the property of distribution is always used when multiplying monomials and polynomials. If you are multiplying a monomial and a polynomial you would use the distributive property to multiply the monomial but the terms of the polynomial. When multiplying a polynomial by a polynomial, it is important to multiply each term of the first polynomial by all of the terms in the second polynomials. Once the expressions are simplified the next step would be to combine like terms. If there is no value for the variable listed, then the expression is complete in its simplified form.
The distribution property becomes important when you are multiplying monomials and polynomials. When you have two sets of polynomials multiplied together, it is important to make sure each part of the expression is simplified. By multiplying every term in the first polynomial by the terms in the second. By doing this you will get what each term equals and then you can simplify the expression.
My example for the class to evaluate is (7x + 2)(3x + 4).
From based off what I was reading in the book it states that the property of distrubution when multiplying monomials and polynomials is commonly and frequently used at all times along with using the product rule when multiplying monomials and polynomials. The reason that the property of distribution is used frequently when multiplying monomials and polynomials is because a monomial consists of one term, whereas a polynomial consists of one or more terms separated by + or - signs and in order to solve these problems in which you need to multiply a monomial by a polynomial, you have to apply the distributive properties and the product rule.
The situations in which distribution would become very important is would be when you are going to have to multiply a monomial by a polynomial, which in that case you would have to apply the distributive properties.
The example I will give the class to use is the following:
12(9x - 18)
When multiplying both monomials and polynomials, you must always use the property of distribution if there is a variable before the parentheses. For instance in the given example: ab(12 +6) you would need to distribute ab to each of the terms in the parentheses, so you would end up with 12ab + 6ab. If there were no variable in front of the parentheses, it would just be simple addition 12 + 6, less the distribution of any other terms so the distributive property would not be necessary. It is important to remember that a monomial usually consists of one term, where a polynomial consists of one or more than one term. However, the polynomial is usually separated by the “+” or “-“signs, but remember you can multiply monomials and polynomials that have more than one variable too. Here is an example for you, the class to solve:
5(15x + 25)