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Factor completely: 4x^(2)(3x+4)-(3x+4) Answer:

Factor completely:\newline4x2(3x+4)−(3x+4) 4 x^{2}(3 x+4)-(3 x+4) \newlineAnswer:

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Full solution

Q. Factor completely:\newline4x2(3x+4)−(3x+4) 4 x^{2}(3 x+4)-(3 x+4) \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in both terms.\newlineThe common factor in 4x2(3x+4)4x^2(3x+4) and −(3x+4)-(3x+4) is (3x+4)(3x+4).
  2. Factor Out Common Factor: Factor out the common factor from both terms.\newlineThe expression can be written as \(3x+44)(44x^22 - 11)\.
  3. Recognize Difference of Squares: Recognize that 4x2−14x^2 - 1 is a difference of squares.\newline4x2−14x^2 - 1 can be factored further since it is a difference of squares: (2x)2−(1)2(2x)^2 - (1)^2.
  4. Factor Difference of Squares: Factor the difference of squares.\newlineThe factored form of 4x2−14x^2 - 1 is (2x+1)(2x−1)(2x + 1)(2x - 1).
  5. Write Completely Factored Form: Write the completely factored form of the original expression.\newlineThe completely factored form of the original expression is (3x+4)(2x+1)(2x−1)(3x+4)(2x+1)(2x-1).

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