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Factor completely: (x-4)(4x-7)-(x-4)^(2)(x-8) Answer:

Factor completely:\newline(x−4)(4x−7)−(x−4)2(x−8) (x-4)(4 x-7)-(x-4)^{2}(x-8) \newlineAnswer:

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Full solution

Q. Factor completely:\newline(x−4)(4x−7)−(x−4)2(x−8) (x-4)(4 x-7)-(x-4)^{2}(x-8) \newlineAnswer:
  1. Identify common factors: Identify common factors in the given expression.\newlineThe expression has (x−4)(x-4) as a common factor in both terms.
  2. Factor out common factor: Factor out the common factor (x−4)(x-4) from the expression.\newlineWe can write the expression as (x−4)[(4x−7)−(x−4)(x−8)].(x-4)[(4x-7) - (x-4)(x-8)].
  3. Distribute and simplify: Distribute the negative sign and simplify the expression inside the brackets.\newlineThis gives us (x−4)[4x−7−(x2−8x+4x−32)](x-4)[4x - 7 - (x^2 - 8x + 4x - 32)].
  4. Combine like terms: Combine like terms inside the brackets.\newlineThis simplifies to (x−4)[4x−7−x2+4x−32](x-4)[4x - 7 - x^2 + 4x - 32].
  5. Continue simplifying: Continue simplifying the expression inside the brackets.\newlineCombine the xx terms to get (x−4)[−x2+8x−7−32](x-4)[-x^2 + 8x - 7 - 32].
  6. Combine constant terms: Combine the constant terms inside the brackets.\newlineThis results in (x−4)[−x2+8x−39](x-4)[-x^2 + 8x - 39].
  7. Final factored form: Since we cannot factor the quadratic expression further, we have the final factored form. The completely factored form of the expression is (x−4)(−x2+8x−39)(x-4)(-x^2 + 8x - 39).

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