Factor 2d^4+6d^3-18d^2-54d

$2 d^{4} + 6 d^{3} - 18 d^{2} - 54 d$

Factor $2 d$ out of $2 d^{4} + 6 d^{3} - 18 d^{2} - 54 d$ .

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Factor $2 d$ out of $2 d^{4}$ .

$2 d (d^{3}) + 6 d^{3} - 18 d^{2} - 54 d$

Factor $2 d$ out of $6 d^{3}$ .

$2 d (d^{3}) + 2 d (3 d^{2}) - 18 d^{2} - 54 d$

Factor $2 d$ out of $- 18 d^{2}$ .

$2 d (d^{3}) + 2 d (3 d^{2}) + 2 d (- 9 d) - 54 d$

Factor $2 d$ out of $- 54 d$ .

$2 d (d^{3}) + 2 d (3 d^{2}) + 2 d (- 9 d) + 2 d (- 27)$

Factor $2 d$ out of $2 d (d^{3}) + 2 d (3 d^{2})$ .

$2 d (d^{3} + 3 d^{2}) + 2 d (- 9 d) + 2 d (- 27)$

Factor $2 d$ out of $2 d (d^{3} + 3 d^{2}) + 2 d (- 9 d)$ .

$2 d (d^{3} + 3 d^{2} - 9 d) + 2 d (- 27)$

Factor $2 d$ out of $2 d (d^{3} + 3 d^{2} - 9 d) + 2 d (- 27)$ .

$2 d (d^{3} + 3 d^{2} - 9 d - 27)$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$2 d ((d^{3} + 3 d^{2}) - 9 d - 27)$

Factor out the greatest common factor (GCF) from each group.

$2 d (d^{2} (d + 3) - 9 (d + 3))$

Factor the polynomial by factoring out the greatest common factor, $d + 3$ .

$2 d ((d + 3) (d^{2} - 9))$

Rewrite $9$ as $3^{2}$ .

$2 d ((d + 3) (d^{2} - 3^{2}))$

Factor.

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Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = d$ and $b = 3$ .

$2 d ((d + 3) ((d + 3) (d - 3)))$

Remove unnecessary parentheses.

$2 d ((d + 3) (d + 3) (d - 3))$

Factor.

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Combine exponents.

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Raise $d + 3$ to the power of $1$ .

$2 d ({(d + 3)}^{1} (d + 3) (d - 3))$

Raise $d + 3$ to the power of $1$ .

$2 d ({(d + 3)}^{1} {(d + 3)}^{1} (d - 3))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 d ({(d + 3)}^{1 + 1} (d - 3))$

Add $1$ and $1$ .

$2 d ({(d + 3)}^{2} (d - 3))$

Remove unnecessary parentheses.

$2 d {(d + 3)}^{2} (d - 3)$