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Factor completely: (x-8)^(6)-2(x-8)^(5) Answer:

Factor completely:\newline(x−8)6−2(x−8)5 (x-8)^{6}-2(x-8)^{5} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(x−8)6−2(x−8)5 (x-8)^{6}-2(x-8)^{5} \newlineAnswer:
  1. Recognize common factor: Recognize the common factor.\newlineIn the expression (x−8)6−2(x−8)5(x-8)^{6}-2(x-8)^{5}, both terms have a common factor of (x−8)5(x-8)^{5}.
  2. Factor out common factor: Factor out the common factor.\newlineFactor (x−8)5(x-8)^{5} out of each term.\newline(x−8)6−2(x−8)5=(x−8)5⋅[(x−8)−2](x-8)^{6}-2(x-8)^{5} = (x-8)^{5} \cdot [(x-8) - 2]
  3. Simplify inside brackets: Simplify the expression inside the brackets.\newlineSubtract 22 from (x−8)(x-8) to get (x−10)(x-10).\newline(x−8)5⋅[(x−8)−2]=(x−8)5⋅(x−10)(x-8)^{5} \cdot [(x-8) - 2] = (x-8)^{5} \cdot (x-10)
  4. Write final factored form: Write the final factored form.\newlineThe completely factored form of the expression is (x−8)5×(x−10)(x-8)^{5} \times (x-10).

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