How to factor the fourth degree polynomial x^4+x^2+2ax+1-a^2

#### Question

#### Answer

Group the terms to form perfect squares

x^4+x^2+2ax+1-a^2

x^4+2x^2+1-x^2+2ax-a^2

(x^2+1)^2-(x-a)^2

Now use the formula for difference of squares

(x^2+x-a+1)(x^2-x+a+1)

How to factor the fourth degree polynomial x^4+x^2+2ax+1-a^2

Group the terms to form perfect squares

x^4+x^2+2ax+1-a^2

x^4+2x^2+1-x^2+2ax-a^2

(x^2+1)^2-(x-a)^2

Now use the formula for difference of squares

(x^2+x-a+1)(x^2-x+a+1)