Krystal Villanueva

2022-02-02

What is Multiplication of Monomials by Polynomials?

Dzikowiec5wa

Beginner2022-02-03Added 13 answers

It works the same as with numbers. For numbers, you know that a(b+c) equals ab+ac.

For the same reason, if you have a monomial and you want to multiplicate it by a polynomial (which is a sum of monomials with some coefficients!), you follow the same rule.

For example, if your monomial is$3{x}^{2}$ , and your polynomial is $3+2x-5{x}^{2}+8{x}^{3}$ , the product is

$3{x}^{2}(3+2x-5{x}^{2})+8{x}^{3}$

you will calculate is as

$3{x}^{2}\cdot 3+3{x}^{2}\cdot 2x-3{x}^{2}\cdot 5{x}^{2}+3{x}^{2}\cdot 8{x}^{3}$ , which is

$9{x}^{2}+6{x}^{3}-15{x}^{4}+24{x}^{5}$

For the same reason, if you have a monomial and you want to multiplicate it by a polynomial (which is a sum of monomials with some coefficients!), you follow the same rule.

For example, if your monomial is

you will calculate is as

rossegues03b

Beginner2022-02-04Added 11 answers

When multiplying polynomials, each term from one polynomial must be multiplied by each term of the other polynomial. Since each term in a polynomial is a monomial, multiplying polynomials becomes multiplying monomials. ... The factors are regrouped, and then multiplied.