Factor completely. y^(6)-x^(2) Answer:

Identify Terms: Step Title: Identify the Terms Concise Step Description: Identify the terms of the expression that need to be factored. Step Calculation: The expression has two terms, y^(6) and -x^(2). Step Output: Terms: y^(6), -x^(2)Recognize Squares: Step Title: Recognize the Difference of Squares Concise Step Description: Recognize that the expression is a difference of two squares. Step Calculation: A difference of squares is in the form a^2 - b^2, which can be factored into (a + b)(a - b). Here, y^(6) is (y^3)^2 and x^(2) is (x)^2. Step Output: Difference of squares: (y^3)^2 - (x)^2Apply Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Apply the difference of squares formula to factor the expression. Step Calculation: Using the formula (a^2 - b^2) = (a + b)(a - b), we get (y^3 + x)(y^3 - x). Step Output: Factored Form: (y^3 + x)(y^3 - x)

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Q. Factor completely.

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y^{6}-x^{2}

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Answer:

Identify Terms: Step Title: Identify the Terms $\newline$ Concise Step Description: Identify the terms of the expression that need to be factored. $\newline$ Step Calculation: The expression has two terms, $y^{6}$ and $-x^{2}$ . $\newline$ Step Output: Terms: $y^{6}$ , $-x^{2}$
Recognize Squares: Step Title: Recognize the Difference of Squares $\newline$ Concise Step Description: Recognize that the expression is a difference of two squares. $\newline$ Step Calculation: A difference of squares is in the form $a^2 - b^2$ , which can be factored into $(a + b)(a - b)$ . Here, $y^{6}$ is $(y^3)^2$ and $x^{2}$ is $(x)^2$ . $\newline$ Step Output: Difference of squares: $(y^3)^2 - (x)^2$
Apply Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Apply the difference of squares formula to factor the expression. $\newline$ Step Calculation: Using the formula $(a^2 - b^2) = (a + b)(a - b)$ , we get $(y^3 + x)(y^3 - x)$ . $\newline$ Step Output: Factored Form: $(y^3 + x)(y^3 - x)$