Solve {l}{16n^{2}-8n^{4}+20n^6}{4n^2(4-3n^2+5n^4)}

$$\left. \begin{array} { l } { 16 n ^ { 2 } - 8 n ^ { 4 } + 20 n ^ { 6 } } \\ { 4 n ^ { 2 } ( 4 - 3 n ^ { 2 } + 5 n ^ { 4 } ) } \end{array} \right.$$

Least Common Multiple

$$100n^{10}-100n^{8}+184n^{6}-80n^{4}+64n^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$16n^{2}-8n^{4}+20n^{6}=4n^{2}\left(5n^{4}-2n^{2}+4\right) 16n^{2}-12n^{4}+20n^{6}=4n^{2}\left(5n^{4}-3n^{2}+4\right)$$

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

$$4n^{2}\left(25n^{8}-25n^{6}+46n^{4}-20n^{2}+16\right)$$

Expand the expression.

$$100n^{10}-100n^{8}+184n^{6}-80n^{4}+64n^{2}$$

Evaluate

$$20n^{6}-8n^{4}+16n^{2},\ 20n^{6}-12n^{4}+16n^{2}$$