Solve {l}{m^2-n^2-m+1}{c+d-c^2+d^2}

$$\left. \begin{array} { l } { m ^ { 2 } - n ^ { 2 } - m + 1 } \\ { c + d - c ^ { 2 } + d ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(c-d-1\right)\left(c+d\right)\left(m^{2}-m-n^{2}+1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$c+d-c^{2}+d^{2}=\left(c-d-1\right)\left(-c-d\right)$$

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

$$\left(c-d-1\right)\left(c+d\right)\left(m^{2}-m-n^{2}+1\right)$$

Expand the expression.

$$c^{2}m^{2}-d^{2}m^{2}-cm^{2}-dm^{2}+md^{2}+cm+dm-mc^{2}+d^{2}n^{2}+cn^{2}+dn^{2}-c^{2}n^{2}-d^{2}+c^{2}-c-d$$

Evaluate

$$m^{2}-m-n^{2}+1,\ d^{2}-c^{2}+c+d$$