Solve {l}{(x-z)(x+z+6y)}{(x-z)(x+z-6y)}{(x+z)(x-z+6y)}{(x+z)(x-z-6y)}

$$\left. \begin{array} { l } { ( x - z ) ( x + z + 6 y ) } \\ { ( x - z ) ( x + z - 6 y ) } \\ { ( x + z ) ( x - z + 6 y ) } \\ { ( x + z ) ( x - z - 6 y ) } \end{array} \right.$$

Least Common Multiple

$$-\left(x^{2}-z^{2}\right)\left(-\left(-6y-z\right)^{2}+x^{2}\right)\left(-\left(6y-z\right)^{2}+x^{2}\right)$$

Solution Steps

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

$$\left(z-x\right)\left(x+z\right)\left(x-6y-z\right)\left(x-6y+z\right)\left(x+6y-z\right)\left(x+6y+z\right)$$

Expand the expression.

$$-x^{6}-1296x^{2}y^{4}-3x^{2}z^{4}+72y^{2}x^{4}-72y^{2}z^{4}+z^{6}+3z^{2}x^{4}+1296z^{2}y^{4}$$

Evaluate

$$\left(x-z\right)\left(x+6y+z\right),\ \left(x-z\right)\left(x-6y+z\right),\ \left(x+z\right)\left(x+6y-z\right),\ \left(x+z\right)\left(x-6y-z\right)$$