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Factor.\newline16r2116r^2 - 1

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Q. Factor.\newline16r2116r^2 - 1
  1. Determine Factoring Technique: Determine the appropriate factoring technique for 16r2116r^2 - 1. Since we have a difference of squares, we can use the formula a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b).
  2. Identify Squares in Expression: Identify the terms in the expression 16r2116r^2 - 1 as squares.\newline16r216r^2 can be written as (4r)2(4r)^2 because 4r×4r=16r24r \times 4r = 16r^2.\newline11 can be written as 121^2 because 1×1=11 \times 1 = 1.\newlineSo, 16r2116r^2 - 1 is in the form of a2b2a^2 - b^2 where a=4ra = 4r and 16r216r^200.
  3. Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression.\newlineUsing a=4ra = 4r and b=1b = 1, we get:\newline(4r)212=(4r1)(4r+1)(4r)^2 - 1^2 = (4r - 1)(4r + 1).
  4. Write Factored Form: Write down the factored form of the expression.\newlineThe factored form of 16r2116r^2 - 1 is (4r1)(4r+1)(4r - 1)(4r + 1).