Factor completely. 16x^(4)y^(6)-1 Answer:

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 two binomials. Step Calculation: Recognize that $16x^4$ is a perfect square, as is $y^6$, and 1 is also a perfect square. The expression can be written as $(4x^2y^3)^2 - 1^2$. Step Output: Expression as a difference of squares: $(4x^2y^3)^2 - 1^2$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 $a = 4x^2y^3$ and $b = 1$, resulting in $(4x^2y^3 - 1)(4x^2y^3 + 1)$. Step Output: Factored form using the difference of squares: $(4x^2y^3 - 1)(4x^2y^3 + 1)$

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Q. Factor completely.

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16 x^{4} y^{6}-1

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Answer:

Recognize Difference of Squares: Step Title: Recognize the Difference of Squares $\newline$ Concise Step Description: Identify that the expression is a difference of squares, which can be factored into the product of two binomials. $\newline$ Step Calculation: Recognize that $16x^4$ is a perfect square, as is $y^6$ , and $1$ is also a perfect square. The expression can be written as $(4x^2y^3)^2 - 1^2$ . $\newline$ Step Output: Expression as a difference of squares: $(4x^2y^3)^2 - 1^2$
Apply Squares Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the difference of squares formula, which states that $a^2 - b^2 = (a - b)(a + b)$ , to factor the expression. $\newline$ Step Calculation: Apply the formula with $a = 4x^2y^3$ and $b = 1$ , resulting in $(4x^2y^3 - 1)(4x^2y^3 + 1)$ . $\newline$ Step Output: Factored form using the difference of squares: $(4x^2y^3 - 1)(4x^2y^3 + 1)$