x4-16×2+4

Rewrite x4 as (x2)2.

(x2)2-16×2+4

Rewrite 16 as 42.

(x2)2-42×2+4

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x2 and b=4.

(x2+4)(x2-4)x2+4

Simplify.

Rewrite 4 as 22.

(x2+4)(x2-22)x2+4

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=2.

(x2+4)(x+2)(x-2)x2+4

(x2+4)(x+2)(x-2)x2+4

(x2+4)(x+2)(x-2)x2+4

Cancel the common factor.

(x2+4)(x+2)(x-2)x2+4

Divide (x+2)(x-2) by 1.

(x+2)(x-2)

(x+2)(x-2)

Apply the distributive property.

x(x-2)+2(x-2)

Apply the distributive property.

x⋅x+x⋅-2+2(x-2)

Apply the distributive property.

x⋅x+x⋅-2+2x+2⋅-2

x⋅x+x⋅-2+2x+2⋅-2

Reorder the factors in the terms x⋅-2 and 2x.

x⋅x-2x+2x+2⋅-2

Add -2x and 2x.

x⋅x+0+2⋅-2

Add x⋅x and 0.

x⋅x+2⋅-2

x⋅x+2⋅-2

Multiply x by x.

x2+2⋅-2

Multiply 2 by -2.

x2-4

x2-4

Divide (x^4-16)/(x^2+4)