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In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.Two definitions of a monomial may be encountered: A monomial, also called a power product or primitive monomial, [1] is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. [2]
It is a polynomial in which no variable occurs to a power of or higher; that is, each monomial is a constant times a product of distinct variables. For example f ( x , y , z ) = 3 x y + 2.5 y − 7 z {\displaystyle f(x,y,z)=3xy+2.5y-7z} is a multilinear polynomial of degree 2 {\displaystyle 2} (because of the monomial 3 x y {\displaystyle 3xy ...
A term is a constant or the product of a constant and one or more variables. Some examples include 7 , 5 x , 13 x 2 y , 4 b {\displaystyle 7,\;5x,\;13x^{2}y,\;4b} The constant of the product is called the coefficient .
where x is a variable we are interested in solving for, we can use cross-multiplication to determine that x = b c d . {\displaystyle x={\frac {bc}{d}}.} For example, suppose we want to know how far a car will travel in 7 hours, if we know that its speed is constant and that it already travelled 90 miles in the last 3 hours.
However, there will be several terms of the form x n−2 y 2, one for each way of choosing exactly two binomials to contribute a y. Therefore, after combining like terms, the coefficient of x n−2 y 2 will be equal to the number of ways to choose exactly 2 elements from an n-element set.
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
A product of monic polynomials is monic. A product of polynomials is monic if and only if the product of the leading coefficients of the factors equals 1. This implies that, the monic polynomials in a univariate polynomial ring over a commutative ring form a monoid under polynomial multiplication.
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...