Which of the following is equivalent to (265)(247)?

Question

Which of the following is equivalent to (265)(247)?

A. 2⁸ − 3²

B. 2⁸ − 3⁴

C. 2¹² − 3²

D. 2¹⁶ − 3⁴

E. 2⁶⁴ − 3⁴

When answering this question, the first step listed is usually the following: (256+9)(256-9)

My question: Where is the +/-9 coming from and how is it related to the difference of squares equation x²-y² = (x+y)(x-y)?

Answer 1

256 = 2⁸

9 = 3²

(265)(247) = (256+9)(256-9) = (2⁸ + 3²)(2⁸ - 3²) = (2⁸)² - (3²)² = 2¹⁶ - 3⁴