Factor 2y^3-54z^3

$2 y^{3} - 54 z^{3}$

Step 1

Factor $2$ out of $2 y^{3} - 54 z^{3}$ .

Factor $2$ out of $2 y^{3}$ .

$2 (y^{3}) - 54 z^{3}$

Factor $2$ out of $- 54 z^{3}$ .

$2 (y^{3}) + 2 (- 27 z^{3})$

Factor $2$ out of $2 (y^{3}) + 2 (- 27 z^{3})$ .

$2 (y^{3} - 27 z^{3})$

Step 2

Rewrite $27 z^{3}$ as ${(3 z)}^{3}$ .

$2 (y^{3} - {(3 z)}^{3})$

Step 3

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

$2 ((y - (3 z)) (y^{2} + y (3 z) + {(3 z)}^{2}))$

Step 4

Factor.

Simplify.

Multiply $3$ by $- 1$ .

$2 ((y - 3 z) (y^{2} + y (3 z) + {(3 z)}^{2}))$

Rewrite using the commutative property of multiplication.

$2 ((y - 3 z) (y^{2} + 3 y z + {(3 z)}^{2}))$

Apply the product rule to $3 z$ .

$2 ((y - 3 z) (y^{2} + 3 y z + 3^{2} z^{2}))$

Raise $3$ to the power of $2$ .

$2 ((y - 3 z) (y^{2} + 3 y z + 9 z^{2}))$

Remove unnecessary parentheses.

$2 (y - 3 z) (y^{2} + 3 y z + 9 z^{2})$

Factor 2y^3-54z^3

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