Question

Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Answer 1

Answer:

D edge

Step-by-step explanation:

Answer 2

Answer:

The correct options, rearranged, are:

Options:

$A)(a^2+ab+b^2)/(a-b)\\\\B)(a^2-ab+b^2)/(a+b)\\\\C)(a^3+0a^2+0ab^2-b^3)/(a+b))\\\\ D)(a^3+0a^2+0ab^2-b^3)/(a-b)$

And the asnwer is the last option (D).

Explanation:

You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.

The difference of two perfect cubes may be represented by:

• $a^3-b^3$

And it is, as a very well known special case:

• $a^3-b^3=(a-b)(a^2+ab+b^2)$

Then, to prove, it you must divide the left side,    $a^3-b^3$     , by the first factor of the right side,    $a-b$

Note that, to preserve the places of each term, you can write:

• $(a^3-b^3)=(a^3+0a^2+0ab^2-b^3)$

Then, you have:

• $(a^3+0a^2+0ab^2-b^3)=(a-b)(a^2+ab+b^2)$

By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:

• $(a^3+0a^2+0ab^2-b^3)/(a-b)=(a^2+ab+b^2)$

That is the last option (D).