What is the result of multiplying the functions f(x) = 4x + 5 and g(x) = 6x + 3 together?

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To find the result of multiplying the functions f(x) = 4x + 5 and g(x) = 6x + 3, you will perform the operation f(x) imes g(x).

Here is the detailed step-by-step process:

  1. First, write down the functions:
    • f(x) = 4x + 5
    • g(x) = 6x + 3
  2. Next, set up the multiplication:
    3. f(x) * g(x) = (4x + 5)(6x + 3)
  3. Now, use the distributive property (also known as the FOIL method for binomials) to expand:
    4. (4x + 5)(6x + 3) = 4x * 6x + 4x * 3 + 5 * 6x + 5 * 3
  4. Calculating each term:
    • 4x * 6x = 24x2
    • 4x * 3 = 12x
    • 5 * 6x = 30x
    • 5 * 3 = 15
  5. Now combine all the terms together:
    6. 24x2 + 12x + 30x + 15
  6. Combine like terms:
    7. 24x2 + (12x + 30x) + 15 = 24x2 + 42x + 15

Thus, the result of multiplying the functions f(x) and g(x) is:

f(x) * g(x) = 24x2 + 42x + 15

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