Solve {l}{(2a^{3}-1)^2}{(a^3-b^2)^2}

$$\left. \begin{array} { l } { ( 2 a ^ { 3 } - 1 ) ^ { 2 } } \\ { ( a ^ { 3 } - b ^ { 2 } ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(\left(2a^{3}-1\right)\left(a^{3}-b^{2}\right)\right)^{2}$$

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.

$$\left(2a^{3}-1\right)^{2}\left(a^{3}-b^{2}\right)^{2}$$

Expand the expression.

$$4a^{12}-4a^{9}+a^{6}-4a^{3}b^{4}+4b^{4}a^{6}+b^{4}-8b^{2}a^{9}+8b^{2}a^{6}-2b^{2}a^{3}$$

Evaluate

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