Solve frac{(x^{3}+y^{3}+z^{3})^{2}-(x^{3}-y^{3}-z^3)^2}{y^3+z^3}

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

Evaluate

$$4x^{3}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \left(y+z\right)\left(y^{2}-yz+z^{2}\right) in both numerator and denominator.

$$2^{2}x^{3}$$

Expand the expression.

$$4x^{3}$$

Expand

$$4x^{3}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \left(y+z\right)\left(y^{2}-yz+z^{2}\right) in both numerator and denominator.

$$2^{2}x^{3}$$

Expand the expression.

$$4x^{3}$$