Solve {l}{(x^2-7)^2-6}{(x^2-7)-27}

$$\left. \begin{array} { l } { ( x ^ { 2 } - 7 ) ^ { 2 } - 6 } \\ { ( x ^ { 2 } - 7 ) - 27 } \end{array} \right.$$

Least Common Multiple

$$\left(x^{2}-34\right)\left(x^{4}-14x^{2}+43\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$\left(x^{2}-7\right)^{2}-6=\left(x^{2}-\left(\sqrt{6}+7\right)\right)\left(x^{2}-\left(-\sqrt{6}+7\right)\right)$$

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

$$\left(x^{2}-34\right)\left(x^{4}-14x^{2}+43\right)$$

Expand the expression.

$$x^{6}-48x^{4}+519x^{2}-1462$$

Evaluate

$$\left(x^{2}-7\right)^{2}-6,\ x^{2}-34$$