Solve [(3x^{2}+y^2)^2-y*y^3]div(-2x)^2

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

Evaluate

$$\frac{3y^{2}}{2}+\frac{9x^{2}}{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

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

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

Calculate -2 to the power of 2 and get 4.

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

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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

Expand

$$\frac{3y^{2}}{2}+\frac{9x^{2}}{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

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

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

Calculate -2 to the power of 2 and get 4.

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

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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