Solve {l}{sqrt{20^2}+x^2}{+sqrt{30^2}+(x-1)^2}{50}

$$\left. \begin{array} { l } { \sqrt { 20 ^ { 2 } } + x ^ { 2 } } \\ { + \sqrt { 30 ^ { 2 } } + ( x - 1 ) ^ { 2 } } \\ { 50 } \end{array} \right.$$

Least Common Multiple

$$50\left(x^{2}+20\right)\left(x^{2}-2x+31\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$50=2\times 5^{2}$$

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

$$50\left(x^{2}+20\right)\left(x^{2}-2x+31\right)$$

Expand the expression.

$$50x^{4}-100x^{3}+2550x^{2}-2000x+31000$$

Evaluate

$$x^{2}+20,\ \left(x-1\right)^{2}+30,\ 50$$