Factor completely: a^(6)-64v^(6) Answer:

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Factor completely:  a^(6)-64v^(6) Answer:

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Recognize as difference of squares: Recognize the expression as a difference of two squares. The expression a^(6) - 64v^(6) can be written as (a^(3))^2 - (8v^(3))^2, which is a difference of two squares since (a^(3))^2 is the square of a^(3) and (8v^(3))^2 is the square of 8v^(3).Apply squares formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a + b)(a - b). Here, a = a^(3) and b = 8v^(3). So, we can factor the expression as follows: (a^(3) + 8v^(3))(a^(3) - 8v^(3))Recognize as cubes: Recognize that both factors are differences and sums of cubes. Both a^(3) + 8v^(3) and a^(3) - 8v^(3) can be further factored because they are sums and differences of cubes, respectively. The sum of cubes formula is a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2).Apply sum of cubes formula: Apply the sum of cubes formula to the first factor. Using the sum of cubes formula on a^(3) + 8v^(3), we get: a^(3) + 8v^(3) = a^(3) + (2v)^(3) = (a + 2v)(a^2 - a(2v) + (2v)^2) Simplifying, we get: (a + 2v)(a^2 - 2av + 4v^2)Apply difference of cubes formula: Apply the difference of cubes formula to the second factor. Using the difference of cubes formula on a^(3) - 8v^(3), we get: a^(3) - 8v^(3) = a^(3) - (2v)^(3) = (a - 2v)(a^2 + a(2v) + (2v)^2) Simplifying, we get: (a - 2v)(a^2 + 2av + 4v^2)Combine factored forms: Combine the factored forms of both factors. Now we combine the factored forms from Step 4 and Step 5 to get the completely factored form of the original expression: (a + 2v)(a^2 - 2av + 4v^2)(a - 2v)(a^2 + 2av + 4v^2)

Factor completely: $\newline$ $a^{6}-64 v^{6}$ $\newline$ Answer:

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