Question

Starting with the formula for the difference of cubes, which pair of steps can be used to show that the expressions are

Answer 1

Answer:

A

Step-by-step explanation:

i learned this before

Answer 2

Answer:

Apply the distributive property, and then combine like terms.

Step-by-step explanation:

First, we know that the formula for the difference of cubes is:

$x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$

So, two show that both parts are equivalent, we just have to apply distributive property on the right side of the equation, because there's a product between a binomial expression and a trinomial expression, here commutative property doesn't make sense.

$x^{3}-y^{3}=x^{3}+x^{2}y+xy^{2}-yx^{2}-xy^{2}-y^{3}$

You can see that almost all terms are eliminated, except the first and last one, the other ones are just subtracted, they are equal but opposite.

Then, we reduce or combine like terms, having the equivalence.

$x^{3}-y^{3}=x^{3}-y^{3}$

Therefore, the correct answer is the first one.