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