Simplify : `9x^(4)+(2x^(3)-5x^(4))-5x^(3)-(x^(4)-3x^(2))` and find its value for x= -2`.

Answer

To simplify the expression \( 9x^4 + (2x^3 - 5x^4) - 5x^3 - (x^4 - 3x^2) \) and find its value for \( x = -2 \), we can follow these steps:

### Step 1: Remove the brackets
We start with the expression:
\[ 9x^4 + (2x^3 - 5x^4) - 5x^3 - (x^4 - 3x^2) \]
Distributing the negative sign across the last bracket:
\[ 9x^4 + 2x^3 - 5x^4 - 5x^3 - x^4 + 3x^2 \]

### Step 2: Combine like terms
Now, we will combine the like terms. The like terms are those with the same power of \( x \):
- For \( x^4 \): \( 9x^4 - 5x^4 - x^4 = (9 - 5 - 1)x^4 = 3x^4 \)
- For \( x^3 \): \( 2x^3 - 5x^3 = (2 - 5)x^3 = -3x^3 \)
- For \( x^2 \): \( 3x^2 \) (there's only one term)

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

### Step 3: Factor out common terms
We can factor out the common factor \( 3 \):
\[ 3(x^4 - x^3 + x^2) \]

### Step 4: Substitute \( x = -2 \)
Now, we will substitute \( x = -2 \) into the simplified expression:
\[ 3((-2)^4 - (-2)^3 + (-2)^2) \]

Calculating each term:
- \( (-2)^4 = 16 \)
- \( (-2)^3 = -8 \)
- \( (-2)^2 = 4 \)

Substituting these values back into the expression:
\[ 3(16 - (-8) + 4) = 3(16 + 8 + 4) = 3(28) \]

### Step 5: Calculate the final value
Now, we multiply:
\[ 3 \times 28 = 84 \]

Thus, the simplified expression is \( 3(x^4 - x^3 + x^2) \) and the value for \( x = -2 \) is \( 84 \).