Solve {l}{-a^{3}+(a^{2}-2b+m^{3})^{2}-(m^{2}-a)^{3}-(2b-a^{2})^{2}-3am^{2}(m^{2}-a)}{(1/2x^{2}-2y)^2-(1/2x-1)(1/2x+1)(1/4x^2+1)-x^2(frac{3}{16}x^2-2y)}

$$\left. \begin{array} { l } { - a ^ { 3 } + ( a ^ { 2 } - 2 b + m ^ { 3 } ) ^ { 2 } - ( m ^ { 2 } - a ) ^ { 3 } - ( 2 b - a ^ { 2 } ) ^ { 2 } - 3 a m ^ { 2 } ( m ^ { 2 } - a ) } \\ { ( \frac { 1 } { 2 } x ^ { 2 } - 2 y ) ^ { 2 } - ( \frac { 1 } { 2 } x - 1 ) ( \frac { 1 } { 2 } x + 1 ) ( \frac { 1 } { 4 } x ^ { 2 } + 1 ) - x ^ { 2 } ( \frac { 3 } { 16 } x ^ { 2 } - 2 y ) } \end{array} \right.$$

Least Common Multiple

$$-2\left(4y^{2}+1\right)\left(a^{2}-2b\right)m^{3}$$

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.

$$-2\left(4y^{2}+1\right)\left(a^{2}-2b\right)m^{3}$$

Expand the expression.

$$-8a^{2}y^{2}m^{3}+16by^{2}m^{3}-2a^{2}m^{3}+4bm^{3}$$

Evaluate

$$2\left(a^{2}-2b\right)m^{3},\ 4y^{2}+1$$