Question

Find the quotient of the quantity negative 6 times x to the 2nd power times y to the 8th power plus 12 times x times y to the 3rd power minus 36 times x times y to the 2nd power all over 6 times x times y to the 2nd power.

Answer 1

[ - 6 * x^2 * y^8 + 12*  x * y^3 - 36 * x * y^2 ] / [6*x*y^2] =

[-6x^2 y^8 ] / [6xy^2] + [12x y^3] / [6xy^2] - [36xy^2] / [6xy^2] =

- xy^6 + 2y - 6

Answer: - xy^6 + 2y - 6

Answer 2

Answer:

The quotient is:

                    $xy^6+2y-6$

Step-by-step explanation:

We are asked to find the quotient of the mathematical expression which is given in terms of variable x and y is represented as:

$=\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}$

Here the numerator is:

$6x^2y^8+12xy^3-36xy^2$

and the denominator is:

$6xy^2$

We can also represent our numerator term by the method of factoring it as:

$6x^2y^8+12xy^3-36xy^2=6xy^2(xy^6+2y-6)$

Hence, our expression gets converted by replacing the numerator term to:

$\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=\dfrac{6xy^2(xy^6+2y-6)}{6xy^2}\\\\\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=xy^6+2y-6$

                 Hence, the quotient is:

                  $xy^6+2y-6$