Solve {l}{5y^{4}-x^{4}}{2y^{4}+4x^{4}}{4*y^{4}}{5*x^4*y^4}{5x^4y^4}

$$\left. \begin{array} { l } { 5 y ^ { 4 } - x ^ { 4 } } \\ { 2 y ^ { 4 } + 4 x ^ { 4 } } \\ { 4 \cdot y ^ { 4 } } \\ { 5 \cdot x ^ { 4 } \cdot y ^ { 4 } } \\ { 5 x ^ { 4 } y ^ { 4 } } \end{array} \right.$$

Least Common Multiple

$$-20\left(5y^{4}-x^{4}\right)\left(2x^{4}+y^{4}\right)\left(xy\right)^{4}$$

Solution Steps

Factor the expressions that are not already factored.

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

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$20x^{4}y^{4}\left(-2x^{4}-y^{4}\right)\left(5y^{4}-x^{4}\right)$$

Expand the expression.

$$-180x^{8}y^{8}-100x^{4}y^{12}+40y^{4}x^{12}$$

Evaluate

$$5y^{4}-x^{4},\ 2\left(2x^{4}+y^{4}\right),\ 4y^{4},\ 5\left(xy\right)^{4},\ 5\left(xy\right)^{4}$$