Factor completely: 1-d^(6) Answer:

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Factor completely:  1-d^(6) Answer:

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Recognize Difference of Squares: Step Title: Recognize the Difference of Squares Concise Step Description: Identify that the expression is a difference of squares, which can be factored into the product of a sum and difference. Step Calculation: Recognize that $1 - d^6$ can be written as $1^2 - (d^3)^2$.Apply Squares Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula $a^2 - b^2 = (a + b)(a - b)$ to factor the expression. Step Calculation: Factor $1^2 - (d^3)^2$ into $(1 + d^3)(1 - d^3)$.Factor Difference of Squares: Step Title: Factor the Resulting Difference of Squares Concise Step Description: Recognize that $1 - d^3$ is also a difference of cubes and can be further factored. Step Calculation: Factor $1 - d^3$ using the difference of cubes formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ to get $(1 - d)(1 + d + d^2)$.Combine Factored Forms: Step Title: Combine the Factored Forms Concise Step Description: Combine the factored forms from the previous steps to write the completely factored expression. Step Calculation: The completely factored form is $(1 + d^3)(1 - d)(1 + d + d^2)$.

Factor completely: $\newline$ $1-d^{6}$ $\newline$ Answer:

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Factor completely: $\newline$ $1-d^{6}$ $\newline$ Answer: