Subtract `7x^(3)+3x^(2)+8x+16` from `9x^(3)+6x^(2)-6x+20`

Answer

To solve the problem of subtracting \( 7x^3 + 3x^2 + 8x + 16 \) from \( 9x^3 + 6x^2 - 6x + 20 \), we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ 9x^3 + 6x^2 - 6x + 20 \]
We need to subtract:
\[ 7x^3 + 3x^2 + 8x + 16 \]

### Step 2: Rewrite the subtraction
To subtract the second polynomial from the first, we rewrite it as:
\[ 9x^3 + 6x^2 - 6x + 20 - (7x^3 + 3x^2 + 8x + 16) \]

### Step 3: Distribute the negative sign
Now, we distribute the negative sign across the terms in the second polynomial:
\[ 9x^3 + 6x^2 - 6x + 20 - 7x^3 - 3x^2 - 8x - 16 \]

### Step 4: Combine like terms
Next, we combine the like terms:
- For \(x^3\) terms: \(9x^3 - 7x^3 = 2x^3\)
- For \(x^2\) terms: \(6x^2 - 3x^2 = 3x^2\)
- For \(x\) terms: \(-6x - 8x = -14x\)
- For constant terms: \(20 - 16 = 4\)

Putting it all together, we have:
\[ 2x^3 + 3x^2 - 14x + 4 \]

### Final Answer
Thus, the result of subtracting \( 7x^3 + 3x^2 + 8x + 16 \) from \( 9x^3 + 6x^2 - 6x + 20 \) is:
\[ \boxed{2x^3 + 3x^2 - 14x + 4} \]