Answer:
(x^5 - 4) (x^10 + 4 x^5 + 16)
Step-by-step explanation:
Factor the following:
x^15 - 64
Hint: | Express x^15 - 64 as a difference of cubes.
x^15 - 64 = (x^5)^3 - 4^3:
(x^5)^3 - 4^3
Hint: | Factor the difference of two cubes.
Factor the difference of two cubes. (x^5)^3 - 4^3 = (x^5 - 4) ((x^5)^2 + x^5 4 + 4^2):
(x^5 - 4) ((x^5)^2 + 4 x^5 + 4^2)
Hint: | For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^5)^2.
Multiply exponents. (x^5)^2 = x^(5×2):
(x^5 - 4) (x^(5×2) + 4 x^5 + 4^2)
Hint: | Multiply 5 and 2 together.
5×2 = 10:
(x^5 - 4) (x^10 + 4 x^5 + 4^2)
Hint: | Evaluate 4^2.
4^2 = 16:
Answer: (x^5 - 4) (x^10 + 4 x^5 + 16)
