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

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

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Full solution

Q. Factor completely:\newline(8x+1)2−(x−2)2 (8 x+1)^{2}-(x-2)^{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). Here, a=(8x+1)a = (8x + 1) and b=(x−2)b = (x - 2).
  2. Apply formula: Apply the difference of squares formula.\newlineUsing the formula (a+b)(a−b)(a + b)(a - b), we substitute aa and bb with (8x+1)(8x + 1) and (x−2)(x - 2), respectively.\newlineSo, the factored form is ((8x+1)+(x−2))((8x+1)−(x−2))((8x + 1) + (x - 2))((8x + 1) - (x - 2)).
  3. Simplify each binomial: Simplify each binomial.\newlineFirst binomial: (8x+1)+(x−2)=8x+x+1−2=9x−1(8x + 1) + (x - 2) = 8x + x + 1 - 2 = 9x - 1.\newlineSecond binomial: (8x+1)−(x−2)=8x−x+1+2=7x+3(8x + 1) - (x - 2) = 8x - x + 1 + 2 = 7x + 3.
  4. Write final factored form: Write the final factored form.\newlineThe expression is now factored completely as (9x−1)(7x+3)(9x - 1)(7x + 3).

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