Solve {l}{m^6-1}{4a^2x^2-4abx+b^2}

$$\left. \begin{array} { l } { m ^ { 6 } - 1 } \\ { 4 a ^ { 2 } x ^ { 2 } - 4 a b x + b ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(m^{2}-1\right)\left(2ax-b\right)^{2}\left(\left(m^{2}+1\right)^{2}-m^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$m^{6}-1=\left(m-1\right)\left(m+1\right)\left(m^{2}+m+1\right)\left(m^{2}-m+1\right)$$

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

$$\left(m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)\left(m^{2}+m+1\right)\left(2ax-b\right)^{2}$$

Expand the expression.

$$4a^{2}x^{2}m^{6}-4a^{2}x^{2}-4abxm^{6}+4abx+b^{2}m^{6}-b^{2}$$

Evaluate

$$\left(m^{2}-1\right)\left(\left(m^{2}+1\right)^{2}-m^{2}\right),\ \left(2ax-b\right)^{2}$$