Solve x^{2}-y^{2}-1,y^2-1-x^2,1-x^2-y^2

$$x ^ { 2 } - y ^ { 2 } - 1 , y ^ { 2 } - 1 - x ^ { 2 } , 1 - x ^ { 2 } - y ^ { 2 }$$

Least Common Multiple

$$\left(x^{2}-y^{2}-1\right)\left(-\left(y^{2}-1\right)^{2}+x^{4}\right)$$

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.

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

Expand the expression.

$$x^{6}-x^{4}-x^{2}y^{4}+2x^{2}y^{2}-x^{2}+y^{6}-y^{4}-y^{2}x^{4}-y^{2}+1$$

Evaluate

$$x^{2}-y^{2}-1,-x^{2}+y^{2}-1,1-y^{2}-x^{2}$$