Multiplying monomials, or one term times one term, is the most simplistic way to multiply polynomials. To correctly solve a math problem involving the multiplication of monomials, first you must multiply the constants, or the numeral digits in the equation. After multiplying the constants, multiply the variables and put the two results together. For example, if you were to multiply 5xy(3y), or 5xy times 3y, first you would multiply 5 and 3 which makes 15. Then you would multiply xy and y to get xy squared. Your answer would be 15xy squared.
To multiply a monomial times a binomial, the rules are the same. Simply multiply the monomial to each term of the binomial. To start, find the polynomial that is made up of only one term, the monomial. Multiply the monomial by the first term of the polynomial. Multiply the monomial by the second term of the polynomial. Combine these answers. For example, to multiply x(2x + xy), multiply x by 2x to get 2x squared. Multiply x by xy to get x squared y. Combine to get the answer of 2 x squared + x squared y.
To multiply two binomials correctly, you must be sure to multiply each term. Multiply the first terms, the outer terms, the inner terms and the last terms. A helpful acronym to remember the order in which to multiply is FOIL, which stand for first, outer, inner, last. To multiply two binomials, multiply the first term of the first polynomial by the first term in the second. Then, multiply the first term of the first polynomial by the second set of terms in the second polynomial. Multiply the second term in the first polynomial by the first term in the second polynomial and finish by multiplying the second term of the first polynomial by the second term in the second polynomial.
Multiplying a binomial and a trinomial is not much different from multiplying any other polynomials. The process just has more steps. To multiply a binomial and a trinomial, multiply each term of the trinomial by each term of the binomial and combine the like terms. To finish, add any like terms that result. For example, to multiply (x + 3y)(2x - 2y + 5), first multiply x by each term between the second set of parentheses to get 2 x squared, -2xy and 5x. Then multiply 3y by each set of terms in the second polynomial to get 6xy, -6y squared and 15y. Combine the terms to get the answer of 2 x squared + 4xy + 5x - 6y squared + 15.