Solve {l}{m^2-n^2}{a^2-16}{x^2-100}

$$\left. \begin{array} { l } { m ^ { 2 } - n ^ { 2 } } \\ { a ^ { 2 } - 16 } \\ { x ^ { 2 } - 100 } \end{array} \right.$$

Least Common Multiple

$$-\left(a^{2}-16\right)\left(x^{2}-100\right)\left(m^{2}-n^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$m^{2}-n^{2}=\left(m+n\right)\left(m-n\right) -16+a^{2}=\left(a-4\right)\left(a+4\right) x^{2}-100=\left(x-10\right)\left(x+10\right)$$

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

$$-\left(a-4\right)\left(x-10\right)\left(a+4\right)\left(m-n\right)\left(x+10\right)\left(m+n\right)$$

Expand the expression.

$$a^{2}n^{2}x^{2}-a^{2}m^{2}x^{2}+16m^{2}x^{2}-16n^{2}x^{2}+100a^{2}m^{2}-100a^{2}n^{2}-1600m^{2}+1600n^{2}$$

Evaluate

$$m^{2}-n^{2},\ a^{2}-16,\ x^{2}-100$$