Factor completely: 1-c^(9) Answer:

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Factor completely:  1-c^(9) Answer:

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Identify type and technique: Identify the type of expression and the appropriate factoring technique. The expression 1 - c^(9) is a difference of two squares, since 1 can be written as 1^2 and c^(9) can be written as (c^(3))^2. The difference of squares can be factored using the formula a^2 - b^2 = (a - b)(a + b).Write in squared form: Write the expression in the form of a^2 - b^2. 1 - c^(9) can be written as (1)^2 - (c^(3))^2.Apply difference of squares: Apply the difference of squares formula. Using the formula a^2 - b^2 = (a - b)(a + b), we get: (1)^2 - (c^(3))^2 = (1 - c^(3))(1 + c^(3)).Recognize sum of cubes: Recognize that 1 + c^(3) is a sum of cubes and can be further factored. The sum of cubes can be factored using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2). However, since we have 1 - c^(3) and 1 + c^(3), we only need to factor 1 + c^(3) as a sum of cubes.Factor sum of cubes: Factor 1 + c^(3) using the sum of cubes formula. 1 + c^(3) can be written as (1)^3 + (c)^3, which factors to: (1 + c)((1)^2 - 1*c + c^2) = (1 + c)(1 - c + c^2).Combine for final expression: Combine the factored forms to get the final factored expression. The final factored form of 1 - c^(9) is: (1 - c^(3))(1 + c)(1 - c + c^2).

Factor completely: $\newline$ $1-c^{9}$ $\newline$ Answer:

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