Factor completely: 27s^(6)-8h^(6) Answer:

Identify Expression Type: Step Title: Identify the Type of Expression Concise Step Description: Recognize that the expression is a difference of two cubes. Step Calculation: The expression 27s^6 - 8h^6 can be rewritten as (3s^2)^3 - (2h^2)^3.Apply Cubes Formula: Step Title: Apply the Difference of Cubes Formula Concise Step Description: Use the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2) to factor the expression. Step Calculation: Let a = 3s^2 and b = 2h^2. Then, apply the formula to get (3s^2 - 2h^2)((3s^2)^2 + (3s^2)(2h^2) + (2h^2)^2).Simplify Factored Expression: Step Title: Simplify the Factored Expression Concise Step Description: Simplify the terms inside the second set of parentheses. Step Calculation: Simplify to get (3s^2 - 2h^2)(9s^4 + 6s^2h^2 + 4h^4).

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Q. Factor completely:

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27 s^{6}-8 h^{6}

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Answer:

Identify Expression Type: Step Title: Identify the Type of Expression $\newline$ Concise Step Description: Recognize that the expression is a difference of two cubes. $\newline$ Step Calculation: The expression $27s^6 - 8h^6$ can be rewritten as $(3s^2)^3 - (2h^2)^3$ .
Apply Cubes Formula: Step Title: Apply the Difference of Cubes Formula $\newline$ Concise Step Description: Use the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ to factor the expression. $\newline$ Step Calculation: Let $a = 3s^2$ and $b = 2h^2$ . Then, apply the formula to get $(3s^2 - 2h^2)((3s^2)^2 + (3s^2)(2h^2) + (2h^2)^2)$ .
Simplify Factored Expression: Step Title: Simplify the Factored Expression $\newline$ Concise Step Description: Simplify the terms inside the second set of parentheses. $\newline$ Step Calculation: Simplify to get $(3s^2 - 2h^2)(9s^4 + 6s^2h^2 + 4h^4)$ .