Factor 432+250m^3

$432 + 250 m^{3}$

Step 1

Factor $2$ out of $432 + 250 m^{3}$ .

Factor $2$ out of $432$ .

$2 (216) + 250 m^{3}$

Factor $2$ out of $250 m^{3}$ .

$2 (216) + 2 (125 m^{3})$

Factor $2$ out of $2 (216) + 2 (125 m^{3})$ .

$2 (216 + 125 m^{3})$

Step 2

Rewrite $216$ as $6^{3}$ .

$2 (6^{3} + 125 m^{3})$

Step 3

Rewrite $125 m^{3}$ as ${(5 m)}^{3}$ .

$2 (6^{3} + {(5 m)}^{3})$

Step 4

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 6$ and $b = 5 m$ .

$2 ((6 + 5 m) (6^{2} - 6 (5 m) + {(5 m)}^{2}))$

Step 5

Factor.

Simplify.

Raise $6$ to the power of $2$ .

$2 ((6 + 5 m) (36 - 6 (5 m) + {(5 m)}^{2}))$

Multiply $5$ by $- 6$ .

$2 ((6 + 5 m) (36 - 30 m + {(5 m)}^{2}))$

Apply the product rule to $5 m$ .

$2 ((6 + 5 m) (36 - 30 m + 5^{2} m^{2}))$

Raise $5$ to the power of $2$ .

$2 ((6 + 5 m) (36 - 30 m + 25 m^{2}))$

Remove unnecessary parentheses.

$2 (6 + 5 m) (36 - 30 m + 25 m^{2})$

Factor 432+250m^3

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