Question

Please answer and explain your reasoning thanks!

Answer 1

The first one is the correct answer.
When you multiply, you end up with 49x^16+28xy^40-28x^40 -16y^64
The two middle terms cancel out so you end up with 49x^16-16^64.

Answer 2

`a^2-b^2=(a-b)(a+b)`

This formula will be useful in helping us factor this.


`49x^(16)-16y^(64)`

This is the equation that we are going to factor.
Let's first change this equation to have the form
`a^2-b^2`

In order to do that, here are two important exponent rules that was used.

`(a^b)^c=a^(bc)`

`(ab)^c=a^c b^c`

With those rules, we can change the equation into the following:

`(7x^8)^2-(4y^(32))^2`

Refer back to the formula I showed in the beginning of this answer.

`a^2-b^2=(a-b)(a+b)`


`(7x^8)^2-(4y^(32))^2=(7x^8-4y^(32))(7x^8-4y^(32))`

Thus, your answer is the first choice. Hope this helps! :)