How to factor the difference a^4-b^16?

We'll use the power
property:

a^4 = a^2*2 =
(a^2)^2

b^16 = b^2*8 =
(b^8)^2

we'll write the terms in this
way:

(a^2)^2 - (b^8)^2

We
notice that we've get a difference of squares:

x^2 - y^2 =
(x-y)(x+y)

We'll put x = a^2 and y =
b^8:

(a^2)^2 - (b^8)^2 = (a^2 - b^8)(a^2 + b^8)
(1)

We notice that the factor a^2 - b^8 is also a
difference of squares:

a^2 - b^8 = (a)^2 -
(b^4)^2

(a)^2 - (b^4)^2 = (a - b^4)(a + b^4)
(2)

We'll substitute (2) in
(1):

a^4-b^16 = (a - b^4)(a + b^4)(a^2 +
b^8)