Question

What is the factorization of 216x12 – 64?

(6x3 – 4)(36x6 + 24x3 + 16)
(6x3 – 4)(36x9 + 24x3 + 16)
(6x4 – 4)(36x8 + 24x4 + 16)
(6x4 – 4)(36x12 + 24x4 + 16)

Answer 1

Hello there!

This is a difference of cubes of the form:

(a^3-b^3) which always factors to (a-b)(a^2+ab+b^2)

So if you find the cube of each term you will have a and b for the factors above.

(216x^12)^(1/3)=6x^4 and 64^(1/3)=4 so

(6x^4-4)(36x^8+24x^4+16), So C. is the correct answer.

Answer 2

216x¹² - 64
8(27x¹²) - 8(8)
8(27x¹² - 8)
8(27x¹² + 18x⁶ - 18x⁶ + 12x⁴ - 12x⁴ - 8)
8(27x¹² + 18x⁸ + 12x⁴ - 18x⁸ - 12x⁴ - 8)
8[3x⁴(9x⁸) + 3x⁴(6x⁴) + 3x⁴(4) - 2(9x⁶) - 2(6x⁴) - 2(4)]
8[3x⁴(9x⁸ + 6x⁴ + 4) - 2(9x⁸ + 6x⁴ + 4)]
8(3x⁴ - 2)(9x⁸ + 6x⁴ + 4)

The answer is C.