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

f(x) - g(x) = -x⁸ + 8x³ + 5x² - 13

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Combining like terms

Step-by-step explanation:

Step 1: Define

f(x) = -5x⁹ - x⁸ + 3x³ - 8

g(x) = -5x⁹ - 5x³ - 5x² + 5

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

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

And we have our final answer!

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