The difference of cubes?

J

jklslc

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Jul 4, 2019
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Hi, I'm new here. I'm an adult in my late 30's trying to reteach myself all the math I did 20 year ago, but haven't used since (haha). No homework or tests or anything; this is merely mental exercise to keep my brain active. Here is my issue...

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, and 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. The rule states that in the trinomial the first and last terms are the squares of the cubed roots. The cubed root of y^3 = y, right? So wouldn't the square of that be y^2? Any help would be appreciated. Thanks so much - I am glad I found this forum.
 
jklslc said:
Hi, I'm new here. I'm an adult in my late 30's trying to reteach myself all the math I did 20 year ago, but haven't used since (haha). No homework or tests or anything; this is merely mental exercise to keep my brain active. Here is my issue...

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, and 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. The rule states that in the trinomial the first and last terms are the squares of the cubed roots. The cubed root of y^3 = y, right? So wouldn't the square of that be y^2? Any help would be appreciated. Thanks so much - I am glad I found this forum.
Click to expand...
As far as I can tell - you are correct and the "key" is wrong.

You can confirm the correctness of your answer by multiplying it out and comparing it with the starting (given) expression [y^6-13y^3+40].

If you multiply out the answer given in the key - you would see that highest exponent of "y" in that answer would be 7 (→ y7)
 
jklslc said:
… squares of the cubed roots. The cubed root of y^3 = y …
Click to expand...
Hi jklslc. Welcome to the forum. Here's a quick note about notation. We say 'cube root', not cubed root. Just like we say 'square root' instead of squared root.

A cubed root might look like this: ?3

Cheers

?
 
jklslc said:
ha...not quite the reply I was looking for but thanks ;-)
Click to expand...
You're welcome! I'm glad you're willing to accept constructive criticism. (A number of people here aren't.)

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