Solve {l}{ab(x-y)-bc(x-y)}{a^4-27a^2+1}

$$\left. \begin{array} { l } { a b ( x - y ) - b c ( x - y ) } \\ { a ^ { 4 } - 27 a ^ { 2 } + 1 } \end{array} \right.$$

Least Common Multiple

$$b\left(a-c\right)\left(x-y\right)\left(a^{4}-27a^{2}+1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$a^{4}-27a^{2}+1=\left(a^{2}-\left(-\frac{5}{2}\sqrt{29}+\frac{27}{2}\right)\right)\left(a^{2}-\left(\frac{5}{2}\sqrt{29}+\frac{27}{2}\right)\right)$$

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

$$b\left(a-c\right)\left(x-y\right)\left(a^{4}-27a^{2}+1\right)$$

Expand the expression.

$$bxa^{5}-bcxa^{4}+27bcxa^{2}-27bxa^{3}+abx-bcx+bcya^{4}-bya^{5}-27bcya^{2}+27bya^{3}+bcy-aby$$

Evaluate

$$b\left(a-c\right)\left(x-y\right),\ a^{4}-27a^{2}+1$$