Question

Given

f(x) = −5x9 − x8 + 3x3 − 8
and
g(x) = −5x9 − 5x3 − 5x2 + 5,
find and simplify
f(x) − g(x).

Answer 1

f(x) - g(x) = -x⁸ + 8x³ + 5x² - 13

General Formulas and Concepts:

Pre-Algebra

• Equality Properties

Algebra I

• Combining like terms

Explanation:

Step 1: Define

f(x) = -5x⁹ - x⁸ + 3x³ - 8

g(x) = -5x⁹ - 5x³ - 5x² + 5

Step 2: Find f(x) - g(x)

1. Substitute: f(x) - g(x) = -5x⁹ - x⁸ + 3x³ - 8 - (-5x⁹ - 5x³ - 5x² + 5)
2. Distribute -1: f(x) - g(x) = -5x⁹ - x⁸ + 3x³ - 8 + 5x⁹ + 5x³ + 5x² - 5
3. CBT (x⁹): f(x) - g(x) = -x⁸ + 3x³ - 8 + 5x³ + 5x² - 5
4. CBT (x³): f(x) - g(x) = -x⁸ + 8x³ - 8 + 5x² - 5
5. CBT (Z): f(x) - g(x) = -x⁸ + 8x³ + 5x² - 13

And we have our final answer!