What is the simplified form of the function 7(x^3+4x)^6(3x^2+4)?

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SUMMARY

The function 7(x^3+4x)^6(3x^2+4) simplifies to 7x^6(x^2+4)^6(3x^2+4). The confusion arises from the misunderstanding of the expression (x^3+4x)^6, which can be rewritten as [x(x^2+4)]^6, leading to the correct simplification. The final form retains the factor of 7 and incorporates the polynomial (3x^2+4) as part of the overall expression.

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h_k331
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According to my text 7(x^3+4x)^6(3x^2+4) simplifies to:

7x^6(x^2+4)^6(3x^2+4)

But it seems to me it should simplify to:

7x(x^2+4)^6(3x^2+4)

What am I missing here?

hk
 
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h_k331 said:
According to my text 7(x^3+4x)^6(3x^2+4) simplifies to:

7x^6(x^2+4)^6(3x^2+4)

But it seems to me it should simplify to:

7x(x^2+4)^6(3x^2+4)

What am I missing here?

hk

[tex](x^3+4x)^6=[x(x^2+4)]^6=x^6(x^2+4)^6[/tex]
 
Ah, now I understand. Thank you saltydog.

hk
 

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