Factor completely. y^(4)-100x^(4) Answer:

Recognize Squares: Step Title: Recognize the Difference of Squares Concise Step Description: Identify that the expression is a difference of two squares. Step Calculation: Recognize that y^(4) is a square (y^2)^2 and 100x^(4) is also a square (10x^2)^2.Apply Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b). Step Calculation: Apply the formula to y^(4) - 100x^(4) to get (y^2 - 10x^2)(y^2 + 10x^2).Factor Further: Step Title: Factor Further if Possible Concise Step Description: Check if the resulting binomials can be factored further. Step Calculation: Notice that y^2 - 10x^2 is also a difference of squares, which can be factored into (y - 10x)(y + 10x). The second binomial y^2 + 10x^2 cannot be factored further over the real numbers.

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Q. Factor completely.

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y^{4}-100 x^{4}

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Answer:

Recognize Squares: Step Title: Recognize the Difference of Squares $\newline$ Concise Step Description: Identify that the expression is a difference of two squares. $\newline$ Step Calculation: Recognize that $y^{4}$ is a square $(y^2)^2$ and $100x^{4}$ is also a square $(10x^2)^2$ .
Apply Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Step Calculation: Apply the formula to $y^{4} - 100x^{4}$ to get $(y^2 - 10x^2)(y^2 + 10x^2)$ .
Factor Further: Step Title: Factor Further if Possible $\newline$ Concise Step Description: Check if the resulting binomials can be factored further. $\newline$ Step Calculation: Notice that $y^2 - 10x^2$ is also a difference of squares, which can be factored into $(y - 10x)(y + 10x)$ . The second binomial $y^2 + 10x^2$ cannot be factored further over the real numbers.