Question

F(x+h) = (x+h)² + 3(x+h)^3

How would I distribute this?

Answer 1

f(x + h) = 3x³ + x² + 9h²x + 3h³ + h² + 9hx² + 2hx

General Formulas and Concepts:

• Order of Operations: BPEMDAS
• Distributive Property
• Expand by FOIL (First Outside Inside Last)
• Combining like terms

Explanation:

Step 1: Define function

f(x) = x² + 3x³

f(x + h) is x = x + h

Step 2: Simplify

1. Substitute: f(x + h) = (x + h)² + 3(x + h)³
2. Expand by FOILing: f(x + h) = (x² + 2hx + h²) + 3(x + h)³
3. Rewrite: f(x + h) = (x² + 2hx + h²) + 3(x + h)²(x + h)
4. Expand by FOILing: f(x + h) = (x²+2hx+h²) + 3(x² + 2hx + h²)(x+h)
5. Distribute/Expand: f(x + h) = (x²+2hx+h²) + 3(x³+3hx²+3h²x+h³)
6. Distribute 3: f(x + h) = (x²+2hx+h²)+(3x³+9hx²+9h²x+3h³)
7. Combine like terms: f(x + h) = 3x³+x²+9h²x+3h³+h²+9hx²+2hx