(8+9x), (64-81x^2), (8-9x)

LCM is

Did you notice that

(8+9x)(8-9x) = 64 - 81x^2 ?

hint:
what would be the LCM for

6 , 42, and 7 ? , notice 6x7 = 42

Note that when (8+9x) and (8-9x) are multiplied,

(8+9x)(8-9x)
= 64 + 72x - 72x - 81x^2
= 64 - 81x^2

Thus the least common multiple is 64 - 81x^2

hope this helps~ :3

thanks

To find the LCM (Least Common Multiple) of the given expressions: (8+9x), (64-81x^2), and (8-9x), we can start by factoring each expression.

1. Factorizing the expression (8+9x):
The expression (8+9x) cannot be factored any further, as it is in its simplest form.

2. Factorizing the expression (64-81x^2):
We can recognize the expression (64-81x^2) as the difference of squares, where 64 is a perfect square and 81x^2 is a perfect square.
Using the identity a^2 - b^2 = (a+b)(a-b), we can factorize 64-81x^2 as follows:

64 - 81x^2 = (8 - 9x)(8 + 9x)

3. Factorizing the expression (8-9x):
Similarly to the first expression, (8-9x) cannot be factored any further.

Now, we have the factored forms of all three expressions:

(8+9x), (8 - 9x), and (8 - 9x)(8 + 9x)

To find the LCM, we need to determine the highest power of each factor that appears in any of the expressions.

Analyzing the factors:
- The factor (8+9x) appears once in its factored form.
- The factor (8-9x) appears twice in its factored form.

To get the LCM, we need to take the highest power for each factor.
Therefore, the LCM of the given expressions is:

LCM = (8 + 9x)(8 - 9x) = (64 - 81x^2)

So, the LCM is (64 - 81x^2).