What is the product of 3 consecutive even integers if the middle integer is x?

Ah, the mysterious case of the consecutive even integers! So, if the middle integer is x, then the two integers that come before it would be (x-2) and (x+2). The product of these three consecutive even integers would be (x-2) * x * (x+2). But let's not stop there! Why not give these integers some character? Let's call the first integer Bob, the middle integer x, and the last integer Steve. So, the product would be Bob * x * Steve. Now we just need to assign numerical values to Bob and Steve, and voila! We have our product!

To find the product of three consecutive even integers given that the middle integer is represented by x, we can set up the equation as follows:

First integer: x - 2
Middle integer: x
Third integer: x + 2

The product of these three integers can be found by multiplying them together:

Product = (x - 2) * x * (x + 2)

Expanding the equation:

Product = (x^2 - 4) * x

Combining the terms:

Product = x^3 - 4x

Therefore, the product of three consecutive even integers with the middle integer represented by x is x^3 - 4x.

To find the product of 3 consecutive even integers with the middle integer represented as x, we first need to determine the expressions representing the three numbers.

Since the numbers are consecutive even integers, we can express them as x - 2, x, and x + 2. The middle integer is denoted as x, and the other two numbers are obtained by decreasing and increasing x by 2, respectively.

Now, to find the product, we multiply the three integers together:

(x - 2) * x * (x + 2)

Using the distributive property, we can multiply x by each of the terms inside the parentheses:

x(x - 2)(x + 2)

Expanding the expression further:

x(x^2 - 4)

Multiplying x by each term inside the parentheses:

x^3 - 4x

Therefore, the product of 3 consecutive even integers (with the middle integer as x) is given by the expression x^3 - 4x.

So your numbers would be

x-2, x, and x+2 , (even numbers are 2 apart)

"product" is the result of multiplication, so

(x-2)(x)(x+2)
= x(x^2 - 4)
or
= x^3 - 4x

check:
let the 3 numbers be 6,8, and 10, (so x = 8)
product = 6*8*10 = 480
from my formula: (8^3) - 4(8) = 512-32 = 480