Having trouble factoring

3x^9- 75x

first factor out 3x to get

3x(x^8 - 25) now you have a difference of squares, so one more step

3x(x^4 + 5(x^4 - 5)

To factor the expression 3x^9 - 75x, we need to find the greatest common factor (GCF) of the two terms. In this case, both terms have a common factor of 3x, so we can factor that out.

Step 1: Factor out the GCF.
3x^9 - 75x
= 3x(x^8 - 25)

Now we have factored out the 3x, and we are left with the expression (x^8 - 25).

Step 2: Recognize the difference of squares pattern.
The expression (x^8 - 25) is a difference of squares because it can be written as (x^4)^2 - 5^2.

Step 3: Apply the difference of squares formula.
The difference of squares formula states that a^2 - b^2 = (a + b)(a - b). We can use this formula to further factorize our expression.

(x^8 - 25) = ((x^4)^2 - 5^2)
= (x^4 + 5)(x^4 - 5)

Now we have factored the expression completely. The factored form of 3x^9 - 75x is 3x(x^4 + 5)(x^4 - 5).