Solve x^{4}-x^{2}y^2+ay^2-ax^2-x^2+a

$$x ^ { 4 } - x ^ { 2 } y ^ { 2 } + a y ^ { 2 } - a x ^ { 2 } - x ^ { 2 } + a$$

Factor

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

Solution Steps

Do the grouping x^{4}-x^{2}y^{2}+ay^{2}-ax^{2}-x^{2}+a=\left(x^{4}-x^{2}y^{2}-x^{2}\right)+\left(-ax^{2}+ay^{2}+a\right), and factor out x^{2} in the first and -a in the second group.

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

Factor out common term x^{2}-y^{2}-1 by using distributive property.

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

Evaluate

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