Simplify `(4x^2+2x^2-3(x-7)-(-2x^4-2x^2+3x-5))`

Answer

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

### Step 1: Distribute and simplify the terms inside the parentheses
We start by distributing the \(-3\) across the terms in the parentheses \( (x - 7) \):
\[ -3(x - 7) = -3x + 21 \]
Now, we rewrite the expression:
\[ 4x^2 + 2x^2 - 3x + 21 - (-2x^4 - 2x^2 + 3x - 5) \]

### Step 2: Simplify the double negative
Next, we simplify the double negative:
\[ -(-2x^4 - 2x^2 + 3x - 5) = 2x^4 + 2x^2 - 3x + 5 \]
Now, we can rewrite the entire expression:
\[ 4x^2 + 2x^2 - 3x + 21 + 2x^4 + 2x^2 - 3x + 5 \]

### Step 3: Combine like terms
Now, we combine all like terms:
- For \(x^4\): \(2x^4\)
- For \(x^2\): \(4x^2 + 2x^2 + 2x^2 = 8x^2\)
- For \(x\): \(-3x - 3x = -6x\)
- For the constant terms: \(21 + 5 = 26\)

Putting it all together, we have:
\[ 2x^4 + 8x^2 - 6x + 26 \]

### Final Result
Thus, the simplified expression is:
\[ \boxed{2x^4 + 8x^2 - 6x + 26} \]

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