4(x+2)^8 (x-3)^6

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20(x+2)^2 (x-3)^12

note:sorry that the expression on top of the line is so farr

I did this before:

(1/5)[(x+2)/(x-3)]^6

perhaps you like this form:

(x+2)^6
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5(x-3)^6

To simplify the given expression, you need to apply the rules of exponents and simplify both the numerator and denominator separately.

Let's begin by simplifying the numerator:
The numerator is 4(x+2)^8(x-3)^6.

To simplify this, we can use the product rule of exponents: (a^m * b^n) = a^(m+n).
In this case, (x+2)^8 can be expanded as (x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2), and (x-3)^6 can be written as (x-3)(x-3)(x-3)(x-3)(x-3)(x-3).

So, the numerator becomes 4 * (x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2) * (x-3)(x-3)(x-3)(x-3)(x-3)(x-3).

Now, let's simplify the denominator:
The denominator is 20(x+2)^2(x-3)^12.

Similar to the numerator, we can expand (x+2)^2 as (x+2)(x+2) and (x-3)^12 as (x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3).

So, the denominator becomes 20 * (x+2)(x+2) * (x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3).

Now, we can cancel out the common factors in the numerator and denominator.

Cancelling out (x+2)^2 from the numerator and denominator:
4(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3) / 20(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)(x-3)

Further simplifying:
We can simplify the expression by dividing both the numerator and denominator by their greatest common factors (GCF). In this case, the GCF is (x-3)^6:

4(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2) / 20

Now, we divide the numerator by the denominator:

(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2) / 5

Therefore, the simplified expression is:
(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2) / 5