How do you factor 3y^3-x^2
You can't
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To factor the expression 3y^3 - x^2, we can use the difference of cubes formula. The difference of cubes formula states that for any two terms a^3 and b^3, the expression a^3 - b^3 can be factored as (a - b)(a^2 + ab + b^2).
In our case, we have 3y^3 - x^2. This can be seen as a^3 - b^3, where a is 3y and b is x. Let's apply the difference of cubes formula:
3y^3 - x^2 = (3y - x)((3y)^2 + (3y)(x) + (x)^2)
Simplifying the terms within the brackets:
= (3y - x)(9y^2 + 3xy + x^2)
So, the factored form of 3y^3 - x^2 is (3y - x)(9y^2 + 3xy + x^2).