Start this as the difference of two squares:?

Question

a^6 - 64

(A) (a2 - 8) (a + 2) (a2 - 2a + 4)

(B) (a3 - 8) (a + 2) (a + 2a + 4)

(C) (a - 2) (a2 + 2a + 4)(a + 2) (a2 - 2a + 4)

OR

(D) (a2 + 8) (a - 2) (a - 2a + 4)

Answer 1

You can most easily solve a multiple choice question like this without doing the long math by examining clues in the choices as follows:

look at the last terms (numbers) of each of the factors and multiply them together.  This would be the last term in the correct answer and should result in 64.

look at at the first term in each of the factors and multiply them together.  in the correct answer it should result in a^6.

If examine each of the choices given, you will see that only (c) meets this criteria, and you've solved the problem in less than a minute.

hope this helps

Answer 2

a^6-64=

a^6-2^6=

(a^3)^2-(2^3)^2=

[a^3+2^3][a^3-2^3]=

(a+2)(a^2-2a+4)(a-2)(a^2+2a+4).



The ans. is (C)

Answer 3

c

Use the hint, difference of two squares:

(a^3-8)(a^3+8)

Now these can be factored because 8 is a perfect cube

(a^3-2^3)(a^3+2^3)

(a-2)(a²+2a+2²)(a+2)(a²-2a+2²) (which is C because 2² =4)