Question

X^4-4x^2-32
x
4
−4x
2
−32

Answer 1

x2 • (x2 - 32772)

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.