Solve {l}{(2x-4)^2+16}{2(5-x)^2}

$$\left. \begin{array} { l } { ( 2 x - 4 ) ^ { 2 } + 16 } \\ { 2 ( 5 - x ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$4\left(x-5\right)^{2}\left(x^{2}-4x+8\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$4\left(x-2\right)^{2}+16=4\left(x^{2}-4x+8\right)$$

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

$$4\left(x-5\right)^{2}\left(x^{2}-4x+8\right)$$

Expand the expression.

$$4x^{4}-56x^{3}+292x^{2}-720x+800$$

Evaluate

$$4\left(\left(x-2\right)^{2}+4\right),\ 2\left(5-x\right)^{2}$$