Solve {c}{x^{2}-4-sqrt{1}}{x+1}{x^4-1}{-2x^2+x}{-5x^5+4x}{(1-x)^2}

$$\left. \begin{array} { c } { x ^ { 2 } - 4 - \sqrt { 1 } } \\ { x + 1 } \\ { x ^ { 4 } - 1 } \\ { - 2 x ^ { 2 } + x } \\ { - 5 x ^ { 5 } + 4 x } \\ { ( 1 - x ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$x\left(2x-1\right)\left(x+1\right)\left(x-1\right)^{2}\left(x^{2}-5\right)\left(x^{2}+1\right)\left(5x^{4}-4\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{4}-1=\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right) x-2x^{2}=x\left(-2x+1\right) -5x^{5}+4x=x\left(-5x^{4}+4\right)$$

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

$$x\left(2x-1\right)\left(x+1\right)\left(x-1\right)^{2}\left(x^{2}-5\right)\left(x^{2}+1\right)\left(5x^{4}-4\right)$$

Expand the expression.

$$10x^{13}-15x^{12}-45x^{11}+75x^{10}-43x^{9}+27x^{8}+81x^{7}-135x^{6}+53x^{5}-12x^{4}-36x^{3}+60x^{2}-20x$$

Evaluate

$$x^{2}-5,\ x+1,\ x^{4}-1,\ x\left(1-2x\right),\ x\left(4-5x^{4}\right),\ \left(1-x\right)^{2}$$