Simplify (-12x^3y^4+18x^2y^3+6x^2y^2)÷6x^2y^2

$(- 12 x^{3} y^{4} + 18 x^{2} y^{3} + 6 x^{2} y^{2}) \div 6 x^{2} y^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{- 12 x^{3} y^{4} + 18 x^{2} y^{3} + 6 x^{2} y^{2}}{6 x^{2} y^{2}}$

Step 2

Factor $6 x^{2} y^{2}$ out of $- 12 x^{3} y^{4} + 18 x^{2} y^{3} + 6 x^{2} y^{2}$ .

Factor $6 x^{2} y^{2}$ out of $- 12 x^{3} y^{4}$ .

$\frac{6 x^{2} y^{2} (- 2 x y^{2}) + 18 x^{2} y^{3} + 6 x^{2} y^{2}}{6 x^{2} y^{2}}$

Factor $6 x^{2} y^{2}$ out of $18 x^{2} y^{3}$ .

$\frac{6 x^{2} y^{2} (- 2 x y^{2}) + 6 x^{2} y^{2} (3 y) + 6 x^{2} y^{2}}{6 x^{2} y^{2}}$

Factor $6 x^{2} y^{2}$ out of $6 x^{2} y^{2}$ .

$\frac{6 x^{2} y^{2} (- 2 x y^{2}) + 6 x^{2} y^{2} (3 y) + 6 x^{2} y^{2} (1)}{6 x^{2} y^{2}}$

Factor $6 x^{2} y^{2}$ out of $6 x^{2} y^{2} (- 2 x y^{2}) + 6 x^{2} y^{2} (3 y)$ .

$\frac{6 x^{2} y^{2} (- 2 x y^{2} + 3 y) + 6 x^{2} y^{2} (1)}{6 x^{2} y^{2}}$

Factor $6 x^{2} y^{2}$ out of $6 x^{2} y^{2} (- 2 x y^{2} + 3 y) + 6 x^{2} y^{2} (1)$ .

$\frac{6 x^{2} y^{2} (- 2 x y^{2} + 3 y + 1)}{6 x^{2} y^{2}}$

Step 3

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x^{2} y^{2} (- 2 x y^{2} + 3 y + 1)}{6 x^{2} y^{2}}$

Rewrite the expression.

$\frac{x^{2} y^{2} (- 2 x y^{2} + 3 y + 1)}{x^{2} y^{2}}$

Step 4

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2} y^{2} (- 2 x y^{2} + 3 y + 1)}{x^{2} y^{2}}$

Rewrite the expression.

$\frac{y^{2} (- 2 x y^{2} + 3 y + 1)}{y^{2}}$

Step 5

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

$\frac{y^{2} (- 2 x y^{2} + 3 y + 1)}{y^{2}}$

Divide $- 2 x y^{2} + 3 y + 1$ by $1$ .

$- 2 x y^{2} + 3 y + 1$