Solve [(-3xy)^{2}*x^{4}-2x^{2}(3xy^2)^2*y/2]div(-3x^2y)^2

$$[ ( - 3 x y ) ^ { 2 } \cdot x ^ { 4 } - 2 x ^ { 2 } ( 3 x y ^ { 2 } ) ^ { 2 } \cdot \frac { y } { 2 } ] \div ( - 3 x ^ { 2 } y ) ^ { 2 }$$

Evaluate

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

Short Solution Steps

Expand \left(-3xy\right)^{2}.

$$\frac{\left(-3\right)^{2}x^{2}y^{2}x^{4}-2x^{2}\times \left(3xy^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9x^{2}y^{2}x^{4}-2x^{2}\times \left(3xy^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{9x^{6}y^{2}-2x^{2}\times \left(3xy^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Expand \left(3xy^{2}\right)^{2}.

$$\frac{9x^{6}y^{2}-2x^{2}\times 3^{2}x^{2}\left(y^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9x^{6}y^{2}-2x^{2}\times 3^{2}x^{2}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{6}y^{2}-2x^{2}\times 9x^{2}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Multiply 2 and 9 to get 18.

$$\frac{9x^{6}y^{2}-18x^{2}x^{2}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{9x^{6}y^{2}-18x^{4}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Cancel out 2, the greatest common factor in 18 and 2.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{\left(-3x^{2}y\right)^{2}}$$

Expand \left(-3x^{2}y\right)^{2}.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{\left(-3\right)^{2}\left(x^{2}\right)^{2}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{\left(-3\right)^{2}x^{4}y^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{9x^{4}y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{9y^{2}\left(x^{2}-y^{3}\right)x^{4}}{9y^{2}x^{4}}$$

Cancel out 9y^{2}x^{4} in both numerator and denominator.

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

Expand

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

Short Solution Steps

Expand \left(-3xy\right)^{2}.

$$\frac{\left(-3\right)^{2}x^{2}y^{2}x^{4}-2x^{2}\times \left(3xy^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9x^{2}y^{2}x^{4}-2x^{2}\times \left(3xy^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{9x^{6}y^{2}-2x^{2}\times \left(3xy^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Expand \left(3xy^{2}\right)^{2}.

$$\frac{9x^{6}y^{2}-2x^{2}\times 3^{2}x^{2}\left(y^{2}\right)^{2}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9x^{6}y^{2}-2x^{2}\times 3^{2}x^{2}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{6}y^{2}-2x^{2}\times 9x^{2}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Multiply 2 and 9 to get 18.

$$\frac{9x^{6}y^{2}-18x^{2}x^{2}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{9x^{6}y^{2}-18x^{4}y^{4}\times \frac{y}{2}}{\left(-3x^{2}y\right)^{2}}$$

Cancel out 2, the greatest common factor in 18 and 2.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{\left(-3x^{2}y\right)^{2}}$$

Expand \left(-3x^{2}y\right)^{2}.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{\left(-3\right)^{2}\left(x^{2}\right)^{2}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{\left(-3\right)^{2}x^{4}y^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9x^{6}y^{2}-9yx^{4}y^{4}}{9x^{4}y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{9y^{2}\left(x^{2}-y^{3}\right)x^{4}}{9y^{2}x^{4}}$$

Cancel out 9y^{2}x^{4} in both numerator and denominator.

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