Solve {l}{1-m^{3}}{x^2-a^2+2xy+y^2+2ab-b^2}

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

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$-x^{2}m^{3}+x^{2}-2xym^{3}+2xy-y^{2}m^{3}+y^{2}+a^{2}m^{3}+b^{2}m^{3}-2abm^{3}+2ab-a^{2}-b^{2}$$

Evaluate

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