Factor 6k^2h^4-54k^4

$6 k^{2} h^{4} - 54 k^{4}$

Step 1

Factor $6 k^{2}$ out of $6 k^{2} h^{4} - 54 k^{4}$ .

Factor $6 k^{2}$ out of $6 k^{2} h^{4}$ .

$6 k^{2} (h^{4}) - 54 k^{4}$

Factor $6 k^{2}$ out of $- 54 k^{4}$ .

$6 k^{2} (h^{4}) + 6 k^{2} (- 9 k^{2})$

Factor $6 k^{2}$ out of $6 k^{2} (h^{4}) + 6 k^{2} (- 9 k^{2})$ .

$6 k^{2} (h^{4} - 9 k^{2})$

Step 2

Rewrite $h^{4}$ as ${(h^{2})}^{2}$ .

$6 k^{2} ({(h^{2})}^{2} - 9 k^{2})$

Step 3

Rewrite $9 k^{2}$ as ${(3 k)}^{2}$ .

$6 k^{2} ({(h^{2})}^{2} - {(3 k)}^{2})$

Step 4

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

$6 k^{2} ((h^{2} + 3 k) (h^{2} - (3 k)))$

Step 5

Factor.

Multiply $3$ by $- 1$ .

$6 k^{2} ((h^{2} + 3 k) (h^{2} - 3 k))$

Remove unnecessary parentheses.

$6 k^{2} (h^{2} + 3 k) (h^{2} - 3 k)$

Factor 6k^2h^4-54k^4

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