Difference of cubes?

Difference of cubes?

Postby Guest » Wed Jul 03, 2019 7:18 pm

The difference of cubes states that a^3-b^3 = (a-b)(a^2+ab+b^2)

So I have the problem to factor, which is:

y^6-13y^3+40

I factored and got this:

(y^3-8)(y^3-5)

That first term is the difference of cubes so the formula should work, but I used it and got:

(y-2)(y^2+2y+4)(y^3-5) BUT.....

my answer key says it should be (y-2)(y^4+2y+4)(y^3-5)

I don't understand why it's y^4 here. It's probably simple, I know, but I've been doing this stuff all day and I think my brain is fried. I'm in my 30's trying to reteach myself this stuff after a long time of ignoring it. Any help would be appreciated. Thanks.
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Re: difference of cubes?

Postby Baltuilhe » Fri Jul 05, 2019 8:24 am

Good morning!

Your answer is correct!

See:
[tex]y^6-13y^3+40[/tex] is sixth degree, right?
Your answer:
[tex]\left(y-2\right)\cdot\left(y^2+2y+4\right)\cdot\left(y^3-5\right)[/tex]

If you multiply [tex]y\cdot y^2\cdot y^3=y^6[/tex], right?

What happens if you multiply by a [tex]y^4[/tex], instead of [tex]y^2[/tex]?

You got a wrong degree answer (8)!

So, ask to your teacher to review the answer, because it's totally wrong :)

I hope I have helped!

Baltuilhe
 
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Re: Difference of cubes?

Postby Guest » Tue Jul 09, 2019 7:19 am

One quick check is to add the highest powers. In (y- 2)(y^4+ 2y+ 4)(y^3- 5), the "leading power" is 1+ 4+ 3= 8. But the original polynomial had leading power 6, not 8. Yes, it's simple- a simple typo in the answer!
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