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Factor completely: (4x-1)^(2)-(x+10)^(2) Answer:

Factor completely:\newline(4x−1)2−(x+10)2 (4 x-1)^{2}-(x+10)^{2} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(4x−1)2−(x+10)2 (4 x-1)^{2}-(x+10)^{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 (4x−1)2−(x+10)2(4x-1)^{2}-(x+10)^{2}, 'a' is (4x−1)(4x-1) and 'b' is (x+10)(x+10).
  3. Apply formula: Apply the difference of squares formula.\newlineUsing the formula (a+b)(a−b)(a + b)(a - b), we get ((4x−1)+(x+10))((4x−1)−(x+10))((4x-1) + (x+10))((4x-1) - (x+10)).
  4. Simplify expressions: Simplify the expressions inside the parentheses.\newlineSimplify (4x−1)+(x+10)(4x-1) + (x+10) to get 5x+95x + 9.\newlineSimplify (4x−1)−(x+10)(4x-1) - (x+10) to get 3x−113x - 11.
  5. Write factored form: Write the factored form of the expression.\newlineThe factored form is (5x+9)(3x−11)(5x + 9)(3x - 11).

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