Factor completely. 81x^(2)y^(4)-1 Answer:

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Factor completely.  81x^(2)y^(4)-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 $81x^2$ is a perfect square, as is $y^4$, and so is 1. The expression can be written as $(9x)^2 - (1y^2)^2$. Step Output: Expression as a difference of squares: $(9x)^2 - (1y^2)^2$Apply Squares Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$, to factor the expression. Step Calculation: Apply the formula with $a = 9x$ and $b = y^2$, yielding $(9x + y^2)(9x - y^2)$. Step Output: Factored form using the difference of squares: $(9x + y^2)(9x - y^2)$Recognize Another Difference of Squares: Step Title: Recognize Another Difference of Squares Concise Step Description: Identify that one of the factors from the previous step is also a difference of squares. Step Calculation: Recognize that $9x - y^2$ can be written as $(3x)^2 - (y)^2$. Step Output: Expression as a difference of squares: $(3x)^2 - (y)^2$Factor Second Difference of Squares: Step Title: Factor the Second Difference of Squares Concise Step Description: Use the difference of squares formula again to factor the expression $9x - y^2$. Step Calculation: Apply the formula with $a = 3x$ and $b = y$, yielding $(3x + y)(3x - y)$. Step Output: Factored form using the difference of squares: $(3x + y)(3x - y)$Write Completely Factored Form: Step Title: Write the Completely Factored Form Concise Step Description: Combine the factored forms from the previous steps to write the completely factored expression. Step Calculation: The completely factored form is $(9x + y^2)(3x + y)(3x - y)$. Step Output: Completely factored form: $(9x + y^2)(3x + y)(3x - y)$

Factor completely. $\newline$ $81 x^{2} y^{4}-1$ $\newline$ Answer:

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Factor completely.\newline81x2y4−1 81 x^{2} y^{4}-1 81x2y4−1\newlineAnswer:

Factor completely. $\newline$ $81 x^{2} y^{4}-1$ $\newline$ Answer: