Solve {l}{(a^{3}-b^{2})(a^{3}+b^{2})}{(c^4+d^2)(d^2-c^4)}

$$\left. \begin{array} { l } { ( a ^ { 3 } - b ^ { 2 } ) ( a ^ { 3 } + b ^ { 2 } ) } \\ { ( c ^ { 4 } + d ^ { 2 } ) ( d ^ { 2 } - c ^ { 4 } ) } \end{array} \right.$$

Least Common Multiple

$$\left(a^{6}-b^{4}\right)\left(c^{8}-d^{4}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$a^{6}-b^{4}=\left(a^{3}-b^{2}\right)\left(a^{3}+b^{2}\right) d^{4}-c^{8}=\left(-c^{2}+d\right)\left(c^{2}+d\right)\left(c^{4}+d^{2}\right)$$

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

$$\left(c^{2}-d\right)\left(c^{2}+d\right)\left(a^{3}-b^{2}\right)\left(a^{3}+b^{2}\right)\left(c^{4}+d^{2}\right)$$

Expand the expression.

$$a^{6}c^{8}-b^{4}c^{8}+b^{4}d^{4}-d^{4}a^{6}$$

Evaluate

$$a^{6}-b^{4},\ d^{4}-c^{8}$$