Solve {c}{(x^{3}-1)xdy}{(x^{3}-6x^{2}+4)+(10x^3-2x^2-20)}{+x^3-6x^2+4}

$$\left. \begin{array} { c } { ( x ^ { 3 } - 1 ) x d y } \\ { ( x ^ { 3 } - 6 x ^ { 2 } + 4 ) + ( 10 x ^ { 3 } - 2 x ^ { 2 } - 20 ) } \\ { + x ^ { 3 } - 6 x ^ { 2 } + 4 } \end{array} \right.$$

Least Common Multiple

$$dxy\left(x^{3}-1\right)\left(11x^{6}-74x^{5}+48x^{4}+28x^{3}+64x^{2}-64\right)$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$dxy\left(x-1\right)\left(x^{2}+x+1\right)\left(11x^{6}-74x^{5}+48x^{4}+28x^{3}+64x^{2}-64\right)$$

Expand the expression.

$$64dxy+11dyx^{10}-74dyx^{9}+48dyx^{8}+17dyx^{7}+138dyx^{6}-48dyx^{5}-92dyx^{4}-64dyx^{3}$$

Evaluate

$$dxy\left(x^{3}-1\right),\ 11x^{3}-8x^{2}-16,\ x^{3}-6x^{2}+4$$