ddaeeric

2021-01-10

Perform the indicated divisions of polynomials by monomials.
$\frac{-18{x}^{2}{y}^{2}+24{x}^{3}{y}^{2}-48{x}^{2}{y}^{3}}{6xy}$

crocolylec

A polynomial is an expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non-negative integral power.
Here the given polynomial is a trinomial.
To divide a polynomial by monomial, divide each term of the polynomial by the monomial.
Divide the trinomial by the monomial 6xy.
Simplify the terms which are under division.
Calculation:
Consider the polynomial $\frac{-18{x}^{2}{y}^{2}+24{x}^{3}{y}^{2}-48{x}^{2}{y}^{3}}{6xy}$.
Divide each term of the polynomial by the monomial 6xy.
$\frac{-18{x}^{2}{y}^{2}+24{x}^{3}{y}^{2}-48{x}^{2}{y}^{3}}{6xy}=\left(\frac{-18{x}^{2}{y}^{2}}{6xy}\right)+\left(\frac{24{x}^{3}{y}^{2}}{6xy}\right)+\left(\frac{-48{x}^{2}{y}^{3}}{6xy}\right)$
$\left(\frac{-18{x}^{2}{y}^{2}}{6xy}\right)+\left(\frac{24{x}^{3}{y}^{2}}{6xy}\right)+\left(\frac{-48{x}^{2}{y}^{3}}{6xy}\right)=-3xy+4{x}^{2}y-8x{y}^{2}$
The simplified value of the polynomial is $-3xy+4{x}^{2}y-8x{y}^{2}$.
Final statement:
The simplified value of the polynomial after division is equals to $-3xy+4{x}^{2}y-8x{y}^{2}$.

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