Factor 27v^(3)+1 completely. Answer:

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Factor  27v^(3)+1 completely. Answer:

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Identify Type and Approach: Identify the type of expression and the approach to factor it. The expression 27v^3 + 1 is a sum of cubes, which can be factored using the sum of cubes formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).Identify 'a' and 'b': Identify 'a' and 'b' in the sum of cubes formula. In the expression 27v^3 + 1, we can see that 27v^3 is the cube of 3v (since (3v)^3 = 27v^3) and 1 is the cube of 1 (since 1^3 = 1). So, a = 3v and b = 1.Apply Sum of Cubes Formula: Apply the sum of cubes formula. Using the values of 'a' and 'b' from Step 2, we apply the sum of cubes formula: 27v^3 + 1 = (3v)^3 + 1^3 = (3v + 1)((3v)^2 - (3v)(1) + 1^2).Simplify Factored Expression: Simplify the factored expression. Now we simplify the expression inside the parentheses: (3v + 1)(9v^2 - 3v + 1).Check for Further Factoring: Check the factored expression for possible further factoring. The quadratic expression 9v^2 - 3v + 1 does not factor further over the integers, so the factoring is complete.

Factor $27 v^{3}+1$ completely. $\newline$ Answer:

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Factor $27 v^{3}+1$ completely. $\newline$ Answer: