Solve {l}{xyz^{3}-xy^3z+x^3yz}{x^3+2x+x^2+2}

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

Least Common Multiple

$$xyz\left(x+1\right)\left(x^{2}+2\right)\left(x^{2}-y^{2}+z^{2}\right)$$

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.

$$xyz\left(x+1\right)\left(x^{2}+2\right)\left(x^{2}-y^{2}+z^{2}\right)$$

Expand the expression.

$$2xyz^{3}-2xzy^{3}+yx^{3}z^{3}+2yx^{2}z^{3}+yz^{3}x^{4}+yzx^{6}+yzx^{5}+2yzx^{4}+2yzx^{3}-zx^{3}y^{3}-2zx^{2}y^{3}-zy^{3}x^{4}$$

Evaluate

$$xyz\left(x^{2}-y^{2}+z^{2}\right),\ \left(x+1\right)\left(x^{2}+2\right)$$