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

[BTGmoderatorDC]

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

A. 2^8 − 3^2
B. 2^8 − 3^4
C. 2^12 − 3^2
D. 2^16 − 3^4
E. 2^64 − 3^4


OA D

Source: Veritas Prep

[Scott@TargetTestPrep]

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

A. 2^8 − 3^2
B. 2^8 − 3^4
C. 2^12 − 3^2
D. 2^16 − 3^4
E. 2^64 − 3^4


OA D

Solution:

We see that two factors in the product are pretty close to each other; therefore, we can express the the product as a difference of two squares:

(256 + 9)(256 - 9)

256^2 - 9^2

(2^8)^2 - (3^2)^2

2^16 - 3^4

Alternate Solution:

Breaking each answer choice into the difference of squares, we have:

A) 2^8 − 3^2

(2^4 - 3^1)(2^4 + 3^1)

13 x 17

We see that A is not correct.

B) 2^8 − 3^4

Since the expression in B is close in value to the expression in A, we see that B is not correct.

C) 2^12 − 3^2

(2^6 - 3^1)(2^6 + 3^1)

61 x 67

We see that C is not correct.

D) 2^16 − 3^4

(2^8 - 3^2)(2^8 + 3^2)

(247)(265)

We see that D is correct.

Answer: D