Factor completely: v^(9)+1 Answer:

Question

Factor completely:  v^(9)+1 Answer:

Bytelearn · Accepted Answer

Recognize Sum of Cubes: Step Title: Recognize the Sum of Two Cubes Concise Step Description: Identify that the expression is a sum of two cubes, which can be factored using the sum of cubes formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Step Calculation: In this case, v^9 is (v^3)^3 and 1 is 1^3, so we can apply the sum of cubes formula with a = v^3 and b = 1. Step Output: Recognize that v^9 + 1 is a sum of cubes.Apply Sum of Cubes Formula: Step Title: Apply the Sum of Cubes Formula Concise Step Description: Apply the sum of cubes formula to factor the expression. Step Calculation: Using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2) with a = v^3 and b = 1, we get (v^3 + 1)((v^3)^2 - v^3*1 + 1^2). Step Output: Factored form is (v^3 + 1)(v^6 - v^3 + 1).Check Further Factorization: Step Title: Check for Further Factorization Concise Step Description: Check if the resulting factors can be factored further. Step Calculation: The first factor v^3 + 1 is a sum of cubes again, which can be factored further. The second factor v^6 - v^3 + 1 is not easily factorable and does not have any obvious factors. Step Output: The first factor v^3 + 1 can be factored further.Factor First Factor Further: Step Title: Factor the First Factor Further Concise Step Description: Apply the sum of cubes formula again to the first factor. Step Calculation: Using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2) with a = v and b = 1, we get (v + 1)(v^2 - v*1 + 1^2). Step Output: Factored form of the first factor is (v + 1)(v^2 - v + 1).Combine Factored Forms: Step Title: Combine the Factored Forms Concise Step Description: Combine the factored forms of both factors to get the completely factored expression. Step Calculation: The completely factored form is (v + 1)(v^2 - v + 1)(v^6 - v^3 + 1). Step Output: Completely factored form is (v + 1)(v^2 - v + 1)(v^6 - v^3 + 1).

Factor completely: $\newline$ $v^{9}+1$ $\newline$ Answer:

Full solution

More problems from Factor polynomials

Related topics

Factor completely:\newlinev9+1 v^{9}+1 v9+1\newlineAnswer:

Factor completely: $\newline$ $v^{9}+1$ $\newline$ Answer: