Question

How do you factor `2y^3 - 54z^3`?

Answer 1

`2y^{3}-54z^{3}=2(y^{3}-27z^{3})=2(y-3z)(y^{2}+3yz+9z^{2})`

Explanation:

Use the formula for factoring the difference of two cubes:

`a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})` (check this by expanding the right hand side).

For the expression `y^{3}-27z^{3}`, use `a=y` and `b=3z`.