Factor completely. 4x^(6)-1 Answer:

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Factor completely.  4x^(6)-1 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 $4x^6$ is $(2x^3)^2$ and $1$ is $1^2$, so the expression $4x^6 - 1$ is a difference of squares: $(2x^3)^2 - 1^2$.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: Apply the formula with $a = 2x^3$ and $b = 1$ to get $(2x^3 + 1)(2x^3 - 1)$.Factor Further if Possible: Step Title: Factor Further if Possible Concise Step Description: Check if the resulting binomials can be factored further. Step Calculation: The term $2x^3 + 1$ cannot be factored further over the integers. However, $2x^3 - 1$ is again a difference of cubes, which can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.Apply Cubes Formula: Step Title: Apply the Difference of Cubes Formula Concise Step Description: Use the difference of cubes formula to factor $2x^3 - 1$. Step Calculation: Apply the formula with $a = 2x$ and $b = 1$ to get $(2x - 1)((2x)^2 + (2x)(1) + 1^2)$, which simplifies to $(2x - 1)(4x^2 + 2x + 1)$.Combine All Factors: Step Title: Combine All Factors Concise Step Description: Combine all factors to write the completely factored form of the original expression. Step Calculation: The completely factored form is $(2x^3 + 1)(2x - 1)(4x^2 + 2x + 1)$.

Factor completely. $\newline$ $4 x^{6}-1$ $\newline$ Answer:

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Factor completely. $\newline$ $4 x^{6}-1$ $\newline$ Answer: