Algebra Examples

$648 a + 1029 a^{4}$

Step 1

Factor $3 a$ out of $648 a + 1029 a^{4}$ .

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Step 1.1

Factor $3 a$ out of $648 a$ .

$3 a (216) + 1029 a^{4}$

Step 1.2

Factor $3 a$ out of $1029 a^{4}$ .

$3 a (216) + 3 a (343 a^{3})$

Step 1.3

Factor $3 a$ out of $3 a (216) + 3 a (343 a^{3})$ .

$3 a (216 + 343 a^{3})$

Step 2

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

$3 a (6^{3} + 343 a^{3})$

Step 3

Rewrite $343 a^{3}$ as ${(7 a)}^{3}$ .

$3 a (6^{3} + {(7 a)}^{3})$

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 $b = 7 a$ .

$3 a ((6 + 7 a) (6^{2} - 6 (7 a) + {(7 a)}^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

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

$3 a ((6 + 7 a) (36 - 6 (7 a) + {(7 a)}^{2}))$

Step 5.1.2

Multiply $7$ by $- 6$ .

$3 a ((6 + 7 a) (36 - 42 a + {(7 a)}^{2}))$

Step 5.1.3

Apply the product rule to $7 a$ .

$3 a ((6 + 7 a) (36 - 42 a + 7^{2} a^{2}))$

Step 5.1.4

Raise $7$ to the power of $2$ .

$3 a ((6 + 7 a) (36 - 42 a + 49 a^{2}))$

Step 5.2

Remove unnecessary parentheses.

$3 a (6 + 7 a) (36 - 42 a + 49 a^{2})$