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Factor completely: (8x-7)^(2)-(2x+1)^(2) Answer:

Factor completely:\newline(8x−7)2−(2x+1)2 (8 x-7)^{2}-(2 x+1)^{2} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(8x−7)2−(2x+1)2 (8 x-7)^{2}-(2 x+1)^{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 can be factored into (a+b)(a−b)(a + b)(a - b).
  2. Identify 'a' and 'b': Identify 'a' and 'b' in the expression.\newlineIn the expression (8x−7)2−(2x+1)2(8x-7)^{2}-(2x+1)^{2}, 'a' is (8x−7)(8x-7) and 'b' is (2x+1)(2x+1).
  3. Apply formula: Apply the difference of squares formula.\newlineUsing the formula (a2−b2)=(a+b)(a−b)(a^2 - b^2) = (a + b)(a - b), we get:\newline((8x−7)+(2x+1))((8x−7)−(2x+1))((8x-7) + (2x+1))((8x-7) - (2x+1))
  4. Simplify expressions: Simplify the expressions inside the parentheses.\newlineSimplify (8x−7)+(2x+1)(8x-7) + (2x+1) to get 10x−610x - 6.\newlineSimplify (8x−7)−(2x+1)(8x-7) - (2x+1) to get 6x−86x - 8.
  5. Write final factored form: Write the final factored form.\newlineThe factored form of the expression is (10x−6)(6x−8)(10x - 6)(6x - 8).

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