How do you factor $a^3b^6-b^3$ ?

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Answer 1 · 2018-05-16T16:58:01

$b^3(a^3b^3 - b^3)$

$a^3b^6 - b^3$

$b^6 = b^3 cdot b^3$

$(a^3b^3b^3 - b^3)$

factorizing;

$b^3(a^3b^3 - b^3)$

Answer 2 · 2018-05-16T17:00:16

$a^3b^6-b^3=b^3(ab-1)(a^2b^2+ab+1)$

We want to simplify $a^3b^6-b^3$ . The first thing to do is to factor out $b^3$ to give $b^3(a^3b^3-1)$ .

If we look carefully, we can see that $b^3(a^3b^3-1)=b^3((ab)^3-1^3)$ . So now we can use a formula to simplify even more:

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

So

$b^3(a^3b^3-1)=b^3((ab)^3-1^3)=$
$b^3((ab)-1)((ab)^2+2(ab)+1^2)=b^3(ab-1)(a^2b^2+ab+1)$

How do you factor a^3b^6-b^3a^3b^6-b^3?