Factor 125n^(3)-8m^(3) completely. Answer:

Recognize as difference of cubes: Recognize the expression as a difference of cubes. 125n^3 - 8m^3 can be written as (5n)^3 - (2m)^3, since 125 = 5^3 and 8 = 2^3.Apply formula: Apply the difference of cubes formula. The difference of cubes formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, a = 5n and b = 2m.Substitute into formula: Substitute a and b into the formula. Using the formula from Step 2, we get: (5n - 2m)((5n)^2 + (5n)(2m) + (2m)^2)Expand terms: Expand the terms inside the parentheses. Now we calculate each term: (5n)^2 = 25n^2 (5n)(2m) = 10nm (2m)^2 = 4m^2 So the factorization becomes: (5n - 2m)(25n^2 + 10nm + 4m^2)Write final factorized form: Write the final factorized form. The completely factorized form of 125n^3 - 8m^3 is: (5n - 2m)(25n^2 + 10nm + 4m^2)

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Factor
125n^(3)-8m^(3) completely.
Answer:

Factor $125 n^{3}-8 m^{3}$ completely. $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Factor

125 n^{3}-8 m^{3}

completely.

\newline

Answer:

Recognize as difference of cubes: Recognize the expression as a difference of cubes. $125n^3 - 8m^3$ can be written as $(5n)^3 - (2m)^3$ , since $125 = 5^3$ and $8 = 2^3$ .
Apply formula: Apply the difference of cubes formula. $\newline$ The difference of cubes formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ . Here, $a = 5n$ and $b = 2m$ .
Substitute into formula: Substitute $a$ and $b$ into the formula. $\newline$ Using the formula from Step $2$ , we get: $\newline$ $(5n - 2m)((5n)^2 + (5n)(2m) + (2m)^2)$
Expand terms: Expand the terms inside the parentheses. $\newline$ Now we calculate each term: $\newline$ $(5n)^2 = 25n^2$ $\newline$ $(5n)(2m) = 10nm$ $\newline$ $(2m)^2 = 4m^2$ $\newline$ So the factorization becomes: $\newline$ $(5n - 2m)(25n^2 + 10nm + 4m^2)$
Write final factorized form: Write the final factorized form. $\newline$ The completely factorized form of $125n^3 - 8m^3$ is: $\newline$ $(5n - 2m)(25n^2 + 10nm + 4m^2)$