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Factor the following expression completely.

16x^5 - x^3

User Joe Savage
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1 Answer

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To factor the expression 16x^5 - x^3 completely, we can factor out the greatest common factor (GCF) and then look for any additional factors.

Step 1: Factor out the GCF.
The GCF of 16x^5 and -x^3 is x^3. By factoring out x^3, we have:
x^3(16x^2 - 1)

Step 2: Look for additional factors.
Now, we need to examine the expression (16x^2 - 1) to see if it can be factored further. This expression represents the difference of squares, which can be factored as follows:

16x^2 - 1 = (4x)^2 - 1^2
= (4x - 1)(4x + 1)

Therefore, the completely factored form of 16x^5 - x^3 is:
x^3(4x - 1)(4x + 1)

I hope this helps! ;)
User Zeema
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