`(3x^4+2x^3-7)+(4x^6-5x^3+9)`
Which of the following expressions is equivalent to the expressions above?

Options

A. `4x^6+3x^4-3x^3+2`
B. `4x^6+3x^4+7x^3+2`
C. `4x^6+3x^4-5x^3+2`
D. `7x^(10)-3x^3+2`

Answer

To solve the expression \((3x^4 + 2x^3 - 7) + (4x^6 - 5x^3 + 9)\), we will follow these steps:

### Step 1: Write down the expression
We start with the given expression:
\[ (3x^4 + 2x^3 - 7) + (4x^6 - 5x^3 + 9) \]

### Step 2: Remove the parentheses
Since there is a positive sign outside the parentheses, we can write:
\[ 3x^4 + 2x^3 - 7 + 4x^6 - 5x^3 + 9 \]

### Step 3: Combine like terms
Next, we will combine the terms that have the same power of \(x\):
- The \(x^6\) term: \(4x^6\)
- The \(x^4\) term: \(3x^4\)
- The \(x^3\) terms: \(2x^3 - 5x^3 = -3x^3\)
- The constant terms: \(-7 + 9 = 2\)

So, we can rewrite the expression as:
\[ 4x^6 + 3x^4 - 3x^3 + 2 \]

### Step 4: Write the final expression
Now we write the final expression in standard form, starting with the highest power of \(x\):
\[ 4x^6 + 3x^4 - 3x^3 + 2 \]

This is the equivalent expression.

### Final Answer:
The equivalent expression is:
\[ 4x^6 + 3x^4 - 3x^3 + 2 \]

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