Solve {l}{(x-y-z)(y-x-z)}{(z-x-v)}

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

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$-x^{3}-vx^{2}-xy^{2}+2vxy-2xyz+xz^{2}-vy^{2}+2yx^{2}-z^{3}+vz^{2}+zx^{2}+zy^{2}$$

Evaluate

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