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PLEASE HELP IM SO STUCK ILL MARK YOU BRIANLIEST!!! 30 POINTS Given the expression: 6x10 − 96x2 Part A: Rewrite the expression by factoring out the greatest common factor. Part B: Factor the entire expression completely. Show the steps of your work.

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wegnerkolmp2741o

Answer:

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

Step-by-step explanation:

6x^10 − 96x^2

Factor out 6x^2

6x^2 ( x^8 - 16)

Notice that inside the parentheses we have the difference of squares

6x^2 ( x^4 ^2 - 4^2)  a^2 - b^2 = (a-b) (a+b)

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

Notice that x^4-4 is also the difference of squares

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

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

Note also that x^4 + 4 can be factored into (x^2+2x+2)(x^2-2x+2)

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

facundo3141592

The maximum common factor is 6x², and the two factorizations are:

[tex]6*x^{10} - 96*x^2 = 6*x^2*( x^8 - 16) = 6*x^2*(x - \sqrt[8]{16})^4*(x + \sqrt[8]{16})^4[/tex]

How to factorize the given expression?

Here we have the expression:

[tex]6*x^{10} - 96*x^2[/tex]

First, we know that 96/6 = 16

Then we can write the factor [tex]6x^2[/tex] as the maximum common factor between the two terms.

Then we can rewrite:

[tex]6*x^{10} - 96*x^2 = 6*x^2*( x^8 - 16)[/tex]

To completely factorize the expression we factorize the part inside the parenthesis.

[tex]x^8 - 16\\\\x = \pm \sqrt[8]{16}[/tex]

Then we can write:

[tex]6*x^{10} - 96*x^2 = 6*x^2*( x^8 - 16) = 6*x^2*(x - \sqrt[8]{16})^4*(x + \sqrt[8]{16})^4[/tex]

If you want to learn more about factorization:

https://brainly.com/question/11579257

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