Solve {l}{(x-1)^2-(x-1)(x+1)+(x+1)^2}{(r-5)(r+5)^2-(r+5)(r-5)^2}

$$\left. \begin{array} { l } { ( x - 1 ) ^ { 2 } - ( x - 1 ) ( x + 1 ) + ( x + 1 ) ^ { 2 } } \\ { ( r - 5 ) ( r + 5 ) ^ { 2 } - ( r + 5 ) ( r - 5 ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$10\left(r^{2}-25\right)\left(x^{2}+3\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-250+10r^{2}=10\left(r-5\right)\left(r+5\right)$$

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

$$10\left(r-5\right)\left(r+5\right)\left(x^{2}+3\right)$$

Expand the expression.

$$10r^{2}x^{2}-250x^{2}+30r^{2}-750$$

Evaluate

$$x^{2}+3,\ 10\left(r^{2}-25\right)$$