Solve {l}{-a^{4}+2a^{3}-4a^{4}+2a^{2}-3a^{2}}{1+2y^{6}-4y^3-6y^6+4y^3-y^5-9}

$$\left. \begin{array} { l } { - a ^ { 4 } + 2 a ^ { 3 } - 4 a ^ { 4 } + 2 a ^ { 2 } - 3 a ^ { 2 } } \\ { 1 + 2 y ^ { 6 } - 4 y ^ { 3 } - 6 y ^ { 6 } + 4 y ^ { 3 } - y ^ { 5 } - 9 } \end{array} \right.$$

Least Common Multiple

$$a^{2}\left(20a^{2}y^{6}-8ay^{6}+4y^{6}+5a^{2}y^{5}-2ay^{5}+y^{5}+40a^{2}-16a+8\right)$$

Solution Steps

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

$$a^{2}\left(20a^{2}y^{6}-8ay^{6}+4y^{6}+5a^{2}y^{5}-2ay^{5}+y^{5}+40a^{2}-16a+8\right)$$

Expand the expression.

$$20a^{4}y^{6}-8a^{3}y^{6}+4a^{2}y^{6}+a^{2}y^{5}+5a^{4}y^{5}-2a^{3}y^{5}+40a^{4}-16a^{3}+8a^{2}$$

Evaluate

$$a^{2}\left(-5a^{2}+2a-1\right),\ -4y^{6}-y^{5}-8$$