Розкласти на множники вирази. Created by Ivansidorenko. algebra-ru

Розкласти на множники вирази...

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Ответ:

$a)\ \ a^4+9b^4=(a^2)^2+(3b^2)^2=\underbrace {(a^2)^2+(3b^2)^2+2\cdo a^2\cdot 3b^2}_{}-2a^2\cdot 3b^2=\\\\=\underbrace{(a^2+3b^2)^2}-6a^2b^2=(a^2+3b^2)-(\sqrt6ab)^2=\\\\=(a^2+3b^2-\sqrt6ab)(a^2+3b^2+\sqrt6ab)$

$b)\ \ y^5+y+1=y^5+y+1+\underbrace{y^2-y^2}_{0}=(y^5-y^2)+(y^2+y+1)=\\\\=y^2\, \underbrace{(y^3-1)}+(y^2+y+1)=y^2\underbrace{(y-1)(y^2+y+1)}_{y^3-1}+(y^2+y+1)=\\\\=(y^2+y+1)(y^2(y-1)+1)=(y^2+y+1)(y^3-y^2+1)$

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