Solve {l}{x^{4}-a^{2}x^{2}-4x^2+4a^2}{x(a-2)^2-x(3a-2)^2}

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

Least Common Multiple

$$8ax\left(1-a\right)\left(x^{2}-4\right)\left(x^{2}-a^{2}\right)$$

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.

$$8ax\left(1-a\right)\left(x-2\right)\left(x+2\right)\left(x-a\right)\left(x+a\right)$$

Expand the expression.

$$-8a^{2}x^{5}+8ax^{5}+8x^{3}a^{4}-8a^{3}x^{3}+32a^{2}x^{3}-32ax^{3}-32xa^{4}+32xa^{3}$$

Evaluate

$$\left(x^{2}-4\right)\left(x^{2}-a^{2}\right),\ -8ax\left(a-1\right)$$