Question

Angelina factored (x - 4^8 ) and wrote that it was equal to (x^2 - 4^2)^2(x^2 + 4^2). Use complete sentences to explain how you could confirm whether Angela’s solution is correct. Prove your conclusion by multiplying out Angela’s solution.

Answer 1

Are you sure the first part isn't supposed to be (x^8 - 4^8) maybe?
It just doesn't make much sense with the way it's written now.
It's just so trivial.

Answer 2

that's how it's written in my question..

Answer 3

You can take the end result,\[\large\rm (x^2 - 4^2)^2(x^2 + 4^2)\]expand it out (which is the opposite of factoring),
and you should end up with the starting result,
\(\large\rm (x-4^8)\)

If you don't, then the statement about the starting thing factoring into the other stuff is false.

Answer 4

So let's start here,\[\large\rm \color{orangered}{\left(\color{black}{x^2-4^2}\right)^2}\]We want to expand out this square, the orange part.
Remember how to expand a square binomial?\[\large\rm (a-b)^2=(a-b)(a-b)\]Where you multiply all the stuff and the things?

Answer 5

yeah I remember how to do that

Answer 6

so it would be\[(x)^2-(2)^2\] , right?

Answer 7

Crapppp sorry OpenStudy didn't give me the notification >.<

Answer 8

When you expand out a square binomial,
\[\large\rm (a-b)^2=(a-b)(a-b)\]you get four terms,\[\large\rm =a^2-ab-ba+b^2\]But the middle two terms will always combine,\[\large\rm =a^2-2ab+b^2\]

Answer 9

its fine :)

Answer 10

So if we expand out our thing,\[\large\rm \color{orangered}{\left(\color{black}{x^2-4^2}\right)^2}\quad=\quad (x^2)^2-x^24^2-4^2x^2+(4^2)^2\]lot of squares floating around! :O

Answer 11

The middle terms combine,\[\large\rm =(x^2)^2-2(4^2x^2)+(4^2)^2\]

Answer 12

\[\large\rm \color{orangered}{(x^2 - 4^2)^2}(x^2 + 4^2)\]So here is what we've done so far,
we've turned this orange thing into three terms by expanding it,\[\large\rm \color{orangered}{\left((x^2)^2-2(4^2x^2)+(4^2)^2\right)}(x^2 + 4^2)\]

Answer 13

And then we would need to multiply these sets of brackets out.
It's going to be a big mess :d

Answer 14

Oh let's simplify some of the orange stuff a sec,\[\large\rm \color{orangered}{\left(x^4-2(4^2x^2)+4^4\right)}(x^2 + 4^2)\]

Answer 15

Then we would expand out these brackets,
ending up with 6 terms.