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Factor.\newline9c2259c^2 - 25

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Q. Factor.\newline9c2259c^2 - 25
  1. Determine factoring technique: Determine the appropriate factoring technique for 9c2259c^2 - 25. 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 perfect squares: Identify the terms in the expression 9c2259c^2 - 25 as perfect squares.\newline9c29c^2 can be written as (3c)2(3c)^2 because 3c×3c=9c23c \times 3c = 9c^2.\newline2525 can be written as 525^2 because 5×5=255 \times 5 = 25.\newlineSo, 9c2259c^2 - 25 is in the form of a2b2a^2 - b^2 where a=3ca = 3c and 9c29c^200.
  3. Apply difference of squares formula: Apply the difference of squares formula to factor the expression.\newlineUsing a=3ca = 3c and b=5b = 5, we get:\newline(3c)252=(3c5)(3c+5)(3c)^2 - 5^2 = (3c - 5)(3c + 5).
  4. Write final factored form: Write the final factored form of the expression.\newlineThe factored form of 9c2259c^2 - 25 is (3c5)(3c+5)(3c - 5)(3c + 5).