Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four? "   a.12 ⋅ x − 4 b. x − 4 ⋅ 12   c.4(x − 12)   d.12(x − 4)

d. 12(x - 4)

Step-by-step explanation:

"the difference of a number and four" is represented as (x - 4), and now we have to multiply that expression by 12 to get:

12(x - 4).

With these expressions that need to be translated into words, oftentimes we are required to start at the end of the expression and work backwards to the beginning.  I read through the sentence and realized that "the difference between a number and four" was my main expression, and then working backwards to the beginning, I see that I am multiplying that main expression by 12.  Keep that in mind.  A lot of times, this is the way to read these.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18