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Factor.\newline16t2−116t^2 - 1

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Full solution

Q. Factor.\newline16t2−116t^2 - 1
  1. Identify Factoring Technique: Determine the appropriate factoring technique for 16t2−116t^2 - 1.\newlineSince we have a difference of squares, we can use the identity (a2−b2)=(a−b)(a+b)(a^2 - b^2) = (a - b)(a + b).
  2. Identify Squares in Expression: Identify the terms in the expression 16t2−116t^2 - 1 as squares.\newline16t216t^2 can be written as (4t)2(4t)^2 because 4t×4t=16t24t \times 4t = 16t^2.\newline11 can be written as 121^2 because 1×1=11 \times 1 = 1.\newlineSo, 16t2−116t^2 - 1 is in the form of a2−b2a^2 - b^2 where a=4ta = 4t and 16t216t^200.
  3. Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression.\newlineUsing the identity (a2−b2)=(a−b)(a+b)(a^2 - b^2) = (a - b)(a + b), we get:\newline(4t)2−12=(4t−1)(4t+1)(4t)^2 - 1^2 = (4t - 1)(4t + 1).

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