Answer :
Final answer:
To express the given equation in standard form, we expand and collect like terms to get x⁴ - 2x³ - 28x² - 17x + 2 = 0.
Explanation:
To express the given equation in standard form, we need to expand and collect like terms. The equation is (x + 4)² = (x⁴ - 2x³ - 27x² - 9x + 18). By expanding (x + 4)², we get x² + 8x + 16. Writing the equation in standard form, we have x⁴ - 2x³ - 27x² - 9x + 18 - x² - 8x - 16 = 0. Simplifying further, the equation in standard form is x⁴ - 2x³ - 28x² - 17x + 2 = 0. Therefore, the correct option is
(b) x⁴ - 2x³ - 27x² - 9x + 18.
The given equation in standard form (after simplification and organization) is -x⁴ +2x³ +28x² +17x -2 = 0 which does not match any of the given options.
To express the equation in standard form, we have to rearrange the equation, making it equal to zero. First, we expand the left-hand side of the equation; the square of (x + 4) gives us x² + 8x + 16.
Now by bringing the entire expression on the right-hand side of the equation to the left-hand side, the equation becomes: x² + 8x + 16 - x⁴ + 2x³ + 27x² + 9x - 18 = 0. This simplifies to -x⁴ + 2x³ + 28x² + 17x - 2 = 0.
However, the standard form of the equation usually states the terms in decreasing powers of x, so the final answer would be -x⁴ +2x³ +28x² +17x -2 = 0, which does not match any of the given options a, b, c, or d. Thus, the answer might be a misprint.
Learn more about Standard Form of an Equation here:
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