Can somebody please help me with a factoring problem?

Question

Could you please factor the following expression(s)? (one or both is fine...thanks)

y^3 - 27

and

x^4 - 16

Answer 1

y^3 - 27 is the difference of perfect cubes

use this formula:
a^3 - b^3 = (a - b) (a^2 + ab + b^2)

y^3 - 3^3

= (y - 3) (y^2 + 3y + 9)


x^4 - 16

(x^2)^2 - 4^2

use this formula:
a^2 - b^2 = (a - b) (a + b)

(x^2 - 4) (x^2 + 4)

factor again using the same formula:
(x - 2) (x + 2) (x^2 + 4)

Answer 2

y^3 - 27 is a sum of cubes.
y^3 - 27 = (y - 3)(y^2 + 3y - 9)

x^4 - 16 is a difference of squares.
x^4 - 16 = (x^2 + 4)(x^2 - 4) = (x^2 + 4)(x + 2)(x - 2)
Note that the factor (x^2 - 4) was also a difference of squres.

The sum of cubes and the difference of squares are types of binomials for which well known, standardized algorithms exist.

Answer 3

all i know is the second one is
(x^2-4)(x^2+4)