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Combine like terms to complete the equivalent expression. 5x^2 - 9 + 1x + 9x + 10 + (2x^2 - 2) * (7x - 9) *...

Combine like terms to complete the equivalent expression.
5x^2 - 9 + 1x + 9x + 10 + (2x^2 - 2) * (7x - 9) * (-x - 2)
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2x^2 - 2
5x^2 - 9 + 1x + 9x + 10 + (14x^2 - 18x^2) + (14x - 9x) * (9 - 1)

Answer

Solution:

  1. First, simplify the expression inside the parentheses:
    (2x^2 - 2) * (7x - 9) * (-x - 2) / (2x^2 - 2)
  2. Factor out the common terms:
    (2x^2 - 2) = 2(x^2 - 1) = 2(x - 1)(x + 1)
  3. Cancel the common factor (2x^2 - 2) in the numerator and denominator.
  4. Now, simplify the remaining expression:
    5x^2 - 9 + 1x + 9x + 10 + (14x^2 - 18x^2) + (14x - 9x) * (9 - 1)
  5. Combine like terms:
    5x^2 + 14x^2 - 18x^2 = 1x^2
    1x + 9x + (14x - 9x) = 15x
    -9 + 10 + (9 - 1) = 9
  6. The equivalent expression is:
    x^2 + 15x + 9

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