X^4-4x^2-32
x
4
−4x
2
−32

x2 • (x2 - 32772)

Step-by-step explanation:

step 1:  ((x4) -  22x2) -  32768x2

step 2: Pull out like factors :

  x4 - 32772x2  =   x2 • (x2 - 32772)

Factoring:  x2 - 32772

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 32772 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.