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simplify-a-2-b-b-3-2ab-2-a-2-b-4b-3-4ab-3-




Question Number 172513 by Mikenice last updated on 28/Jun/22
simplify  (√(a^2 b+b^3 +2ab^2 )) −(√(a^2 b+4b^3 +4ab^3 ))
simplifya2b+b3+2ab2a2b+4b3+4ab3
Commented by Rasheed.Sindhi last updated on 28/Jun/22
Do you mean:  (√(a^2 b+b^3 +2ab^2 )) −(√(a^2 b+4b^3 +4ab^2 ))
Doyoumean:a2b+b3+2ab2a2b+4b3+4ab2
Commented by Mikenice last updated on 28/Jun/22
yes
yes
Answered by Rasheed.Sindhi last updated on 28/Jun/22
(√(a^2 b+b^3 +2ab^2 )) −(√(a^2 b+4b^3 +4ab^2 ))  =(√(b(a^2 +b^2 +2ab))) −(√(b(a^2 +4b^2 +4ab)))  =(√(b(a+b)^2 )) −(√(b(a+2b)^2 ))  =(√b)((a+b) −(a+2b))  =(√b) (a+b −a−2b))  =−b(√b)
a2b+b3+2ab2a2b+4b3+4ab2=b(a2+b2+2ab)b(a2+4b2+4ab)=b(a+b)2b(a+2b)2=b((a+b)(a+2b))=b(a+ba2b))=bb
Answered by MJS_new last updated on 28/Jun/22
(√(a^2 b+b^3 +2ab^2 ))=∣a+b∣(√b)  (√(a^2 b+4b^3 +4ab^2 ))=∣a+2b∣(√b)  different results depending on a+b and  a+2b >=<0
a2b+b3+2ab2=∣a+bba2b+4b3+4ab2=∣a+2bbdifferentresultsdependingona+banda+2b>=<0

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