Solve {l}{x(x-1)(x-2)-6}{32ac^2+15cx^2-48ax^2-10c^3}

$$\left. \begin{array} { l } { x ( x - 1 ) ( x - 2 ) - 6 } \\ { 32 a c ^ { 2 } + 15 c x ^ { 2 } - 48 a x ^ { 2 } - 10 c ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$\left(x-3\right)\left(16a-5c\right)\left(x^{2}+2\right)\left(3x^{2}-2c^{2}\right)$$

Solution Steps

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

$$\left(x-3\right)\left(16a-5c\right)\left(x^{2}+2\right)\left(3x^{2}-2c^{2}\right)$$

Expand the expression.

$$48ax^{5}-15cx^{5}+45cx^{4}-144ax^{4}-32ac^{2}x^{3}+10c^{3}x^{3}+96ax^{3}-30cx^{3}+96ac^{2}x^{2}-30x^{2}c^{3}+90cx^{2}-288ax^{2}-64axc^{2}+20xc^{3}+192ac^{2}-60c^{3}$$

Evaluate

$$\left(x-3\right)\left(x^{2}+2\right),\ \left(16a-5c\right)\left(2c^{2}-3x^{2}\right)$$