Question

find the quotient of $-18x^{4}y^{4}+36x^{3}y^{3}-24x^{2}y^{2}$ divided by $6xy$.

Explanation:

Step1: Divide each term by \(6xy\)

We have the polynomial \(-18x^{4}y^{4}+36x^{3}y^{3}-24x^{2}y^{2}\) and we divide each term by \(6xy\).
For the first term: \(\frac{-18x^{4}y^{4}}{6xy}\)
For the second term: \(\frac{36x^{3}y^{3}}{6xy}\)
For the third term: \(\frac{-24x^{2}y^{2}}{6xy}\)

Step2: Simplify each term

Simplify \(\frac{-18x^{4}y^{4}}{6xy}\):
Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\) and \(\frac{ab}{cd}=\frac{a}{c}\cdot\frac{b}{d}\), we have \(\frac{-18}{6}\cdot x^{4 - 1}\cdot y^{4 - 1}=- 3x^{3}y^{3}\)

Simplify \(\frac{36x^{3}y^{3}}{6xy}\):
\(\frac{36}{6}\cdot x^{3-1}\cdot y^{3 - 1}=6x^{2}y^{2}\)

Simplify \(\frac{-24x^{2}y^{2}}{6xy}\):
\(\frac{-24}{6}\cdot x^{2-1}\cdot y^{2 - 1}=-4xy\)

Answer:

\(-3x^{3}y^{3}+6x^{2}y^{2}-4xy\)