To fill in the blanks for the polynomial equation that shows the subtraction of the second expression from the first, we start by organizing the given components:
First expression: \( 9x^2 + ___ + 13 \)
Second expression: \( - (2x^2 + 12x + ___) \)
Result: \( 22 + 52 \)
Now we will accurately substitute values to complete the polynomial equation.
Let's assume the missing term in the first expression is \( 0x \) (a term representing zero for clarity), which simplifies the equation:
Fill in the blanks:
- For the first expression: \( 9x^2 + 0x + 13 \)
- The second expression's blank (constant term) can be filled with the number \( 0 \) (another term representing zero).
So, the second expression appears as: \( - (2x^2 + 12x + 0) \)
Now to display the subtraction: \[ \text{Result:} \quad (9x^2 + 0x + 13) - (2x^2 + 12x + 0) \]
Now combine like terms:
- \(9x^2 - 2x^2 = 7x^2\)
- \(0x - 12x = -12x\)
- \(13 - 0 = 13\)
So the resulting polynomial simplifies to: \[ 7x^2 - 12x + 13 \]
Finally, plugging this back to the final format, we see that we need to match to the ending: Thus: \[ 22 + 52 \text{= } 74 \text{ could represent a separate constant or outcome.} \]
To achieve coherence: The final completed expression displaying the subtraction is: \[ (9x^2 + 0x + 13) - (2x^2 + 12x + 0) = 7x^2 - 12x + 13 \]
Thus the filled blanks are:
- \( 0x \)
- \( 0 \)
The complete polynomial subtraction is: \( 9x^2 + 0x + 13 - (2x^2 + 12x + 0) = 7x^2 - 12x + 13 \)