Solve {l}{25x^{2}-10x+1-9y^{2}-6y^2-z^2}{x^4y^4-16}

$$\left. \begin{array} { l } { 25 x ^ { 2 } - 10 x + 1 - 9 y ^ { 2 } - 6 y ^ { 2 } - z ^ { 2 } } \\ { x ^ { 4 } y ^ { 4 } - 16 } \end{array} \right.$$

Least Common Multiple

$$\left(-\left(5x-1\right)^{2}+15y^{2}+z^{2}\right)\left(\left(xy\right)^{4}-16\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{4}y^{4}-16=\left(xy-2\right)\left(xy+2\right)\left(x^{2}y^{2}+4\right)$$

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

$$\left(-25x^{2}+10x+15y^{2}+z^{2}-1\right)\left(xy-2\right)\left(xy+2\right)\left(x^{2}y^{2}+4\right)$$

Expand the expression.

$$15x^{4}y^{6}-x^{4}y^{4}+400x^{2}-160x-25y^{4}x^{6}+10y^{4}x^{5}-240y^{2}+z^{2}x^{4}y^{4}-16z^{2}+16$$

Evaluate

$$\left(5x-1\right)^{2}-15y^{2}-z^{2},\ \left(xy\right)^{4}-16$$