Answered

To whoever answers this (a-b) or (c-d) will get lots of points (i'll give you crown if you answer it all) Common Monomial Factor

To Whoever Answers This Ab Or Cd Will Get Lots Of Points Ill Give You Crown If You Answer It All Common Monomial Factor class=

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Keideviz

✎ Problem:

Factor the following:

  1. 8x⁵y⁷ - 20x³y⁶
  2. 18y⁴ + 30y² - 42y
  3. x⁴ - 1
  4. 81 - p²
  5. y² - 20y + 100
  6. x² + 24x + 144
  7. y³ - 1/27
  8. 27x⁶ - y⁶

✎ Answers:

For Numbers 1 and 2, this involves factoring the common monomial factor which is the common factor, as a product of numerical and literal coefficients all terms in a given polynomial have in common, such that the common factor can be evenly divided into each term.

  • 1. 8x⁵y⁷ - 20x³y⁶ = 4x³y⁶ (2x²y - 5)
  • 2. 18y⁴ + 30y² - 42y = 6y (3y³ + 5y - 7)

For Numbers 3 and 4, this involves factoring the difference of two squares, which is in the form a² - b² = (a + b)(a - b)

  • 3. x⁴ - 1 = (x² + 1)(x² - 1)
  • 4. 81 - p² = (9 + p)(9 - p)

For Numbers 5 and 6, this involves factoring the perfect square trinomial, which is in the form:

  • a² + 2ab + b² = (a + b)²
  • a² - 2ab + b² = (a - b)²

So:

  • 5. y² - 20y + 100 = (y - 10)²
  • 6. x² + 24x + 144 = (x + 12)²

For Numbers 7 and 8, this involves factoring the sum or difference of two cubes, which is in the form:

  • a³ + b³ = (a + b)(a² - ab + b²)
  • a³ - b³ = (a - b)(a² + ab + b²)

So:

  • 7. y³ - 1/27 = (y - 1/3)(y² + y/3 + 1/9)
  • 8. 27x⁶ - y⁶ = (3x² - y²)(9x³ + 3x²y² + y³)

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