Factor 8w^(3)+n^(3) completely. Answer:

Recognize as sum of cubes: Recognize the expression as a sum of two cubes. The given expression is 8w^3 + n^3, which can be written as (2w)^3 + n^3, indicating that it is a sum of cubes.Apply sum of cubes formula: Apply the sum of cubes formula. The sum of cubes formula is a^3 + b^3 = (a + b)(a^2 - ab + b^2). Here, a = 2w and b = n.Substitute into formula: Substitute a and b into the formula. Using the values of a and b, we get (2w + n)((2w)^2 - (2w)(n) + n^2).Expand and simplify terms: Expand and simplify the terms in the second factor. (2w + n)(4w^2 - 2wn + n^2) is the expanded form of the second factor.Write final factorized form: Write the final factorized form. The complete factorization of 8w^3 + n^3 is (2w + n)(4w^2 - 2wn + n^2).

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Factor $8 w^{3}+n^{3}$ completely. $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Factor

8 w^{3}+n^{3}

completely.

\newline

Answer:

Recognize as sum of cubes: Recognize the expression as a sum of two cubes. $\newline$ The given expression is $8w^3 + n^3$ , which can be written as $(2w)^3 + n^3$ , indicating that it is a sum of cubes.
Apply sum of cubes formula: Apply the sum of cubes formula. $\newline$ The sum of cubes formula is $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ . Here, $a = 2w$ and $b = n$ .
Substitute into formula: Substitute $a$ and $b$ into the formula. $\newline$ Using the values of $a$ and $b$ , we get $(2w + n)((2w)^2 - (2w)(n) + n^2)$ .
Expand and simplify terms: Expand and simplify the terms in the second factor. $\newline$ $(2w + n)(4w^2 - 2wn + n^2)$ is the expanded form of the second factor.
Write final factorized form: Write the final factorized form. $\newline$ The complete factorization of $8w^3 + n^3$ is $(2w + n)(4w^2 - 2wn + n^2)$ .