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Factor completely: (x+1)^(2)-(5x-8)^(2) Answer:

Factor completely:\newline(x+1)2−(5x−8)2 (x+1)^{2}-(5 x-8)^{2} \newlineAnswer:

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Factor numerical expressions using the distributive propertyright chevron icon

Full solution

Q. Factor completely:\newline(x+1)2−(5x−8)2 (x+1)^{2}-(5 x-8)^{2} \newlineAnswer:
  1. Recognize as difference of squares: Recognize the expression as a difference of squares. The given expression is in the form of a2−b2a^2 - b^2, which is a difference of squares. The difference of squares can be factored into (a+b)(a−b)(a + b)(a - b).
  2. Identify aa and bb: Identify aa and bb for the difference of squares.\newlineIn the expression (x+1)2−(5x−8)2(x+1)^{2}-(5x-8)^{2}, aa is (x+1)(x+1) and bb is (5x−8)(5x-8).
  3. Apply formula: Apply the difference of squares formula.\newlineUsing the formula (a+b)(a−b)(a + b)(a - b), we can write the factored form of the expression as:\newline((x+1)+(5x−8))((x+1)−(5x−8))((x+1) + (5x-8))((x+1) - (5x-8))
  4. Simplify each factor: Simplify each factor.\newlineFirst factor: (x+1)+(5x−8)=x+1+5x−8=6x−7(x+1) + (5x-8) = x + 1 + 5x - 8 = 6x - 7\newlineSecond factor: (x+1)−(5x−8)=x+1−5x+8=−4x+9(x+1) - (5x-8) = x + 1 - 5x + 8 = -4x + 9
  5. Write final form: Write the final factored form.\newlineThe factored form of the expression is (6x−7)(−4x+9)(6x - 7)(-4x + 9).

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