Is it possible to simplify this further? Watch

Clefairy_Clefairy
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#1
Report Thread starter 11 years ago
#1
Hi there, I was just wondering if anyone could help me simplify this:

(p^3 - q^3) / (p - q)


Thanks
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Zhen Lin
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#2
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Use polynomial long division. First term is p², so that gives you a remainder of p²q - q³, etc.
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Kolya
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#3
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You can factorize p^3 - q^3. (Clearly p=q is a root of that expression)
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Icy_Mikki
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#4
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(Original post by candle_light)
Hi there, I was just wondering if anyone could help me simplify this:

(p^3 - q^3) / (p - q)


Thanks
Hint: p^3 - q^3 = (p-q)(p^2 + pq + q^2)
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Clefairy_Clefairy
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#5
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(Original post by Kolya)
You can factorize p^3 - q^3. (Clearly p=q is a root of that expression)
What do you mean by factorize?... Sorry, being really slow here!
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hippobluecampe
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#6
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p^2 + pq + q^2
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Clefairy_Clefairy
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#7
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(Original post by Icy_Mikki)
Hint: p^3 - q^3 = (p-q)(p^2 + pq + q^2)
How did you get that?!
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studyboy
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#8
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(p^3-q^3)=(p-q)(p^2+pq+q^2)
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studyboy
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#9
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(Original post by candle_light)
How did you get that?!
By inspection, or do long division.
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Clefairy_Clefairy
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#10
Report Thread starter 11 years ago
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(Original post by studyboy)
By inspection, or do long division.
Oh long division, I see. Oh it worked!

Thank you so much

That was actually quite obvious wasn't it?! I think I got freaked out by two variables.
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Daniel Freedman
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#11
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(Original post by candle_light)
Oh long division, I see. Oh it worked!

Thank you so much

That was actually quite obvious wasn't it?! I think I got freaked out by two variables.
It's a good idea to remember the factorisation in Icy Mikki's post.
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studyboy
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#12
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(Original post by candle_light)
Oh long division, I see. Oh it worked!

Thank you so much

That was actually quite obvious wasn't it?! I think I got freaked out by two variables.
You are welcome.
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