BTGmoderatorDC wrote: ↑Fri Jun 26, 2020 6:59 pm
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
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