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Factor completely: (2x-1)^(5)-6(2x-1)^(4) Answer:

Factor completely:\newline(2x−1)5−6(2x−1)4 (2 x-1)^{5}-6(2 x-1)^{4} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(2x−1)5−6(2x−1)4 (2 x-1)^{5}-6(2 x-1)^{4} \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in both terms.\newlineThe common factor is (2x−1)4(2x-1)^{4} because it is present in both terms of the expression.
  2. Factor Out Common Factor: Factor out the common factor (2x−1)4(2x-1)^{4}. We write the expression as (2x−1)4(2x-1)^{4} times the remaining factors. (2x−1)5−6(2x−1)4=(2x−1)4×[(2x−1)−6](2x-1)^{5} - 6(2x-1)^{4} = (2x-1)^{4} \times [(2x-1) - 6]
  3. Simplify Inside Brackets: Simplify the expression inside the brackets.\newlineSubtract 66 from (2x−1)(2x-1) to get the second term of the factored expression.\newline(2x−1)−6=2x−1−6=2x−7(2x-1) - 6 = 2x - 1 - 6 = 2x - 7
  4. Write Final Factored Expression: Write the final factored expression.\newlineThe completely factored form is (2x−1)4×(2x−7)(2x-1)^{4} \times (2x - 7).

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