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write this expression in his completely factored form 27x2−327x^2-3

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Full solution

Q. write this expression in his completely factored form 27x2−327x^2-3
  1. Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression 27x2−327x^2 - 3. The GCF of 27x227x^2 and 33 is 33.
  2. Factor out GCF: Factor out the GCF from the expression. 3(9x2−1)3(9x^2 - 1)
  3. Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. 9x2−19x^2 - 1 can be written as (3x)2−(1)2(3x)^2 - (1)^2, which is a difference of squares.
  4. Apply formula: Apply the difference of squares formula: a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b). Factor the expression inside the parentheses using the difference of squares formula. 3(9x2−1)=3((3x+1)(3x−1))3(9x^2 - 1) = 3((3x + 1)(3x - 1))
  5. Write final factored form: Write the final factored form of the original expression.\newlineThe completely factored form of 27x2−327x^2 - 3 is 3(3x+1)(3x−1)3(3x + 1)(3x - 1).

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