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How do you factor #u^3 - 125v^3#?

Answer 1

#u^3-(5v)^3=(u-5v)(u^2+5uv+25v^2)#

Use the difference of two cubes formula. That is, #(x^3-y^3)=(x-y)(x^2+xy+y^2)#. So first write out the problem as a difference of two cubes then apply the formula.

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Answer 2

Isaiah Anthony

To factor ( u^3 - 125v^3 ), you can use the difference of cubes formula, which states that ( a^3 - b^3 ) can be factored as ( (a - b)(a^2 + ab + b^2) ).

So, ( u^3 - 125v^3 ) can be factored as ( (u - 5v)(u^2 + 5uv + 25v^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.