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How do you factor #27x^3 -8y^3#?

Answer 1

Avery Alexander

#(3x-2y)(9y^2 + 6xy +4y^2)#

We should notice that every part of this expression is a cube. We can factor it as the difference of cubes.

#27x^3 -8y^3#

=#(3x-2y)(9y^2 + 6xy +4y^2)#

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Answer 2

Nathan Axel

To factor the expression (27x^3 - 8y^3), we can use the difference of cubes formula, which states that (a^3 - b^3 = (a - b)(a^2 + ab + b^2)). Applying this formula, we get:

[27x^3 - 8y^3 = (3x)^3 - (2y)^3]

So, (a = 3x) and (b = 2y). Substituting these values into the formula, we have:

[27x^3 - 8y^3 = (3x - 2y)(9x^2 + 6xy + 4y^2)]

Therefore, the factored form of (27x^3 - 8y^3) is ((3x - 2y)(9x^2 + 6xy + 4y^2)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.