prernamalhotra wrote:If ¡n! = (n!)², then ¡17! - ¡16! =

A) ¡1!
B) (¡16!)(¡4!)(2)
C)(¡16!)(12)(2)
D)17^2
E) (¡16!)(12^2)(2)

Aside: This question requires us to factor a DIFFERENCE OF SQUARES
In general a² - b² = (a + b)(a - b)
For example: x² - 9 = (x + 3)(x - 3)

Aside: 17! = (17)(16)(15)...(3)(2)(1)
And 16! = (16)(15)...(3)(2)(1)
So, we can say that 17! = (17)(16!)

Okay, onto the question....
¡17! - ¡16! = (17!)² - (16!)²
= (17! + 16!)(17! - 16!) we factored the difference of squares
= [16!(17 + 1)][16!(17 - 1)] factored 16! from both parts
= [16!(18)][16!(16)]
= (16!)²(18)(16)
= (16!)²(288)
= (16!)²(12)(12)(2)
= (16!)²(12²)(2)
= (¡16!)(12²)(2)
= E

Cheers,
Brent