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Subtract the polynomials. Assume all variable exponents represent whole numbers.

\((3x^{6} + 3x^{5} - 4x^{4} - 8) - (6x^{6} + 7x^{5} + 6x^{4} + 6)\)

Answer :

Putting it all together, the simplified expression is:

-3x^6 - 4x^5 - 10x^4 - 14

To subtract the polynomials, we need to combine like terms. Let's subtract each term one by one:

(3x^6 + 3x^5 - 4x^4 - 8) - (6x^6 + 7x^5 + 6x^4 + 6)

First, let's subtract the x^6 terms:

3x^6 - 6x^6 = -3x^6

Next, subtract the x^5 terms:

3x^5 - 7x^5 = -4x^5

Then, subtract the x^4 terms:

-4x^4 - 6x^4 = -10x^4

Finally, subtract the constant terms:

-8 - 6 = -14

Putting it all together, the simplified expression is:

-3x^6 - 4x^5 - 10x^4 - 14

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