Solve {l}{(x^{1/2}-x^{2})(x^{1/2}+x^{2})}{(4x^frac{4{3}}+9x^frac{1{3}})(3x^frac{5{3}}-2x^frac{2{3}})}

$$\left. \begin{array} { l } { ( x ^ { \frac { 1 } { 2 } } - x ^ { 2 } ) ( x ^ { \frac { 1 } { 2 } } + x ^ { 2 } ) } \\ { ( 4 x ^ { \frac { 4 } { 3 } } + 9 x ^ { \frac { 1 } { 3 } } ) ( 3 x ^ { \frac { 5 } { 3 } } - 2 x ^ { \frac { 2 } { 3 } } ) } \end{array} \right.$$

Least Common Multiple

$$x\left(3x-2\right)\left(4x+9\right)\left(x^{3}-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x-x^{4}=x\left(x-1\right)\left(-x^{2}-x-1\right) -18x+19x^{2}+12x^{3}=x\left(3x-2\right)\left(4x+9\right)$$

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

$$x\left(x-1\right)\left(3x-2\right)\left(4x+9\right)\left(x^{2}+x+1\right)$$

Expand the expression.

$$12x^{6}+19x^{5}-18x^{4}-12x^{3}-19x^{2}+18x$$

Evaluate

$$x\left(1-x^{3}\right),\ x\left(3x-2\right)\left(4x+9\right)$$