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Multiplying polynomials [ edit ] When using algebra tiles to multiply a monomial by a monomial , the student must first set up a rectangle where the length of the rectangle is the one monomial and then the width of the rectangle is the other monomial , similar to when one multiplies integers using algebra tiles.
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 ...
A visual memory tool can replace the FOIL mnemonic for a pair of polynomials with any number of terms. Make a table with the terms of the first polynomial on the left edge and the terms of the second on the top edge, then fill in the table with products of multiplication. The table equivalent to the FOIL rule looks like this:
In algebra, a multilinear polynomial [1] is a multivariate polynomial that is linear (meaning affine) in each of its variables separately, but not necessarily simultaneously. It is a polynomial in which no variable occurs to a power of 2 {\displaystyle 2} or higher; that is, each monomial is a constant times a product of distinct variables.
Thus, any nonzero polynomial p in R has a unique expression = as a linear combination of monomials, where S is a finite subset of M and the c u are all nonzero. When a monomial order has been chosen, the leading monomial is the largest u in S , the leading coefficient is the corresponding c u , and the leading term is the corresponding c u u .
where x is a variable we are interested in solving for, we can use cross-multiplication to determine that =. 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.