can someone please show me how to solve this: (a^n-b^n)/(a-n), and i would also like to know if there's more than one way to do it. Thank you
Thanks for your reply. I'm having trouble trying to figure out how to solve this problem using the long division. I'm feeling like an idiot , can you please show me how to do it. If there's only one variable I can do it in seconds without the calculator but add a second variable and I'm lost.
I figured it out. Here's how to do it: for example if we have (27a^3-8b^3)/(3a-2b)
9a^2
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3a-2b| 27a^3-8b^3
27a^3 /3a =9a^2
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9a^2
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3a-2b| 27a^3-8b^3
27a^3 -18ba^2
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-8b^3 +18ba^2
(9a^2) (3a) =27a^3, (9a^2)(-2b) = -18ba^2
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9a^2 +4b^2
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3a-2b| 27a^3-8b^3
27a^3 -18ba^2
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-8b^3 +18ba^2
(-8b^3)/(-2b)= 4b^2
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9a^2 +4b^2
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3a-2b| 27a^3-8b^3
27a^3 -18ba^2
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-8b^3 +18ba^2
-8b^3 +12ab^2
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(18ba^2)-(12ab^2)
(4b^2)(-2b)= -8b^3, (4b^2)(3a)= 12ab^2
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9a^2 +4b^2 +6ab
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3a-2b| 27a^3-8b^3
27a^3 -18ba^2
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-8b^3 +18ba^2
-8b^3 +12ab^2
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(18ba^2)-(12ab^2)
(18ba^2)/ (3a) = 6ab
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9a^2 +4b^2 +6ab
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3a-2b| 27a^3-8b^3
27a^3 -18ba^2
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-8b^3 +18ba^2
-8b^3 +12ab^2
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(18ba^2)-(12ab^2)
18ba^2 -12ab^2
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(6ab)(3a)= 18ba^2, (6ab)(-2b) = -12ab^2
so the answer is : 9a^2 +6ab+4b^2