Solve {c}{y^{2}+3yz+z^2}{2y^2+yz}{-y^2+2vz+z^2}

$$\left. \begin{array} { c } { y ^ { 2 } + 3 y z + z ^ { 2 } } \\ { 2 y ^ { 2 } + y z } \\ { - y ^ { 2 } + 2 v z + z ^ { 2 } } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$-2y^{6}+6y^{3}z^{3}+5y^{2}z^{4}+10vy^{2}z^{3}+yz^{5}+2vyz^{4}-3z^{2}y^{4}+14vz^{2}y^{3}-7zy^{5}+4vzy^{4}$$

Evaluate

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