# What is this expression equal to?

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1. Dec 22, 2016

### doktorwho

• Member reminded to post homework-type questions in the Homework sections
Basically i need to evaluate the limit of this expression $\lim \sqrt[3]{n^6-n^4+5}-n^2=?$ I want to know if this is correct and why:
$\lim \sqrt[3]{n^6-n^4+5}-n^2=\lim \sqrt[3]{n^6-n^4+5}-n^2*\frac{(\sqrt[3]{n^6-n^4+5})^2+n^2\sqrt[3]{n^6-n^4+5}+n^4}{(\sqrt[3]{n^6-n^4+5})^2+n^2\sqrt[3]{n^6-n^4+5}+n^4}=\lim \frac{n^6-n^4+5-n^6}{(\sqrt[3]{n^6-n^4+5})^2+n^2\sqrt[3]{n^6-n^4+5}+n^4}$
Why does the above fraction equals that? Is that an identity of some kind?

2. Dec 22, 2016

### Staff: Mentor

Is this a schoolwork question? If so, I can move it to the Homework Help forums.

3. Dec 22, 2016

### Math_QED

Do you know the identity:

$a^3 - b^3 = (a - b)(a^2 + ab + b^3)$?

4. Dec 22, 2016

### ehild

You meant $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.

5. Dec 23, 2016

### doktorwho

Its not exactly a homework problem but an already finished problem but i didnt understand that part so was looking for the identity. Thanks

6. Dec 23, 2016

### Math_QED

Ah thanks for correcting the typo.