Solve {l}{2c^{3}+c^{2}d-cd^{2}}{x^3-x^2y-xy^2+y^3}

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

Least Common Multiple

$$-c\left(2c-d\right)\left(c+d\right)\left(x+y\right)\left(x-y\right)^{2}$$

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.

$$-c\left(2c-d\right)\left(c+d\right)\left(x+y\right)\left(x-y\right)^{2}$$

Expand the expression.

$$cd^{2}x^{3}-dc^{2}x^{3}-2c^{3}x^{3}+dxc^{2}y^{2}-cxd^{2}y^{2}+2xy^{2}c^{3}+cd^{2}y^{3}-dc^{2}y^{3}-2c^{3}y^{3}+dyc^{2}x^{2}-cyd^{2}x^{2}+2yx^{2}c^{3}$$

Evaluate

$$c\left(2c-d\right)\left(c+d\right),\ \left(x+y\right)\left(x-y\right)^{2}$$