Krystal Villanueva

2022-02-02

What is Multiplication of Monomials by Polynomials?

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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
$3{x}^{2}\left(3+2x-5{x}^{2}\right)+8{x}^{3}$
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
$9{x}^{2}+6{x}^{3}-15{x}^{4}+24{x}^{5}$

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