Final answer:
The result of subtracting (x - 4)² from 9x² + 2x + 8 is the simplified polynomial 8x² + 10x - 8 in standard form.
Step-by-step explanation:
The question asks for the result of subtracting (x - 4)² from 9x² + 2x + 8, and presenting the result as a simplified polynomial in standard form. Let's expand (x - 4)² first:
(x - 4)² = x² - 8x + 16
Now, we subtract (x² - 8x + 16) from (9x² + 2x + 8):
9x² + 2x + 8 - (x² - 8x + 16)
When we distribute the negative sign through the second polynomial, we get:
9x² + 2x + 8 - x² + 8x - 16
Combine like terms:
(9x² - x²) + (2x + 8x) + (8 - 16)
8x² + 10x - 8
The result in simplified polynomial form in standard order is 8x² + 10x - 8.