Answer :

Sure! Let's simplify the given expression step-by-step:

The expression is:

[tex]\[
(3x^3 - 7x^4 - 3) + (-5x^4 - 9 + 5x^3)
\][/tex]

Step 1: Combine like terms.

1. Identify and combine the [tex]\(x^4\)[/tex] terms:
- We have [tex]\(-7x^4\)[/tex] and [tex]\(-5x^4\)[/tex].
- Combining these gives: [tex]\(-7x^4 + (-5x^4) = -12x^4\)[/tex].

2. Identify and combine the [tex]\(x^3\)[/tex] terms:
- We have [tex]\(3x^3\)[/tex] and [tex]\(5x^3\)[/tex].
- Combining these gives: [tex]\(3x^3 + 5x^3 = 8x^3\)[/tex].

3. Identify and combine the constant terms:
- We have [tex]\(-3\)[/tex] and [tex]\(-9\)[/tex].
- Combining these gives: [tex]\(-3 + (-9) = -12\)[/tex].

Step 2: Write the simplified polynomial using the combined terms.

Putting it all together, the simplified expression is:

[tex]\[
-12x^4 + 8x^3 - 12
\][/tex]

So, the final simplified form of the expression is: [tex]\(-12x^4 + 8x^3 - 12\)[/tex].

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