1Cademy - Factoring $$250m^3 + 432n^3$$

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Strategy to Factor Polynomials Completely

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Factoring $250m^3 + 432n^3$

Factor $250m^3 + 432n^3$ completely.

First, check for a greatest common factor. Both terms share a numerical factor of $2$ . Factor it out: $2(125m^3 + 216n^3)$

Next, the expression inside the parentheses is a binomial. Because $125m^3 = (5m)^3$ and $216n^3 = (6n)^3$ , it is a sum of cubes.

Apply the sum of cubes pattern $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ with $a = 5m$ and $b = 6n$ : $2((5m)^3 + (6n)^3)$ $2(5m + 6n)((5m)^2 - (5m)(6n) + (6n)^2)$

Simplify the trinomial factor to obtain the completely factored form: $2(5m + 6n)(25m^2 - 30mn + 36n^2)$

Multiply to check the result.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.6 Factoring - Intermediate Algebra @ OpenStax

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