Q: Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. In what situations would distribution become important?

A: 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)^.
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).
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