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o-na [289]
3 years ago
5

F(x+h) = (x+h)² + 3(x+h)^3 How would I distribute this?

Mathematics
1 answer:
Leno4ka [110]3 years ago
3 0

Answer:

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

Step-by-step explanation:

<u>Step 1: Define function</u>

f(x) = x² + 3x³

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

<u>Step 2: Simplify</u>

  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
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