Factor completely. 144x^(6)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 $144x^6y^6$ is a perfect square, as is 1, so the expression can be written as $(12x^3y^3)^2 - 1^2$. Step Output: Expression as a difference of squares: $(12x^3y^3)^2 - 1^2$Apply Formula for Factoring: 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 $a = 12x^3y^3$ and $b = 1$ to get $(12x^3y^3 + 1)(12x^3y^3 - 1)$. Step Output: Factored form using the difference of squares: $(12x^3y^3 + 1)(12x^3y^3 - 1)$

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Q. Factor completely.

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144 x^{6} 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 $144x^6y^6$ is a perfect square, as is $1$ , so the expression can be written as $(12x^3y^3)^2 - 1^2$ . $\newline$ Step Output: Expression as a difference of squares: $(12x^3y^3)^2 - 1^2$
Apply Formula for Factoring: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the difference of squares formula $a^2 - b^2 = (a + b)(a - b)$ to factor the expression. $\newline$ Step Calculation: Apply the formula with $a = 12x^3y^3$ and $b = 1$ to get $(12x^3y^3 + 1)(12x^3y^3 - 1)$ . $\newline$ Step Output: Factored form using the difference of squares: $(12x^3y^3 + 1)(12x^3y^3 - 1)$