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abdullinatasano
@abdullinatasano
October 2021
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х^8+х^4+1
a^3-3a+2
х^4+х^2у^2+у^4
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Prosto145
1)x^8+x^4+1 = (x^8+2x^4+1)-x^4=(x^4+1)^2-(x^2)^2=(x^4-x^2+1)(x^4+x^2+1)=
=(x^4-x^2+1)((x^2+1)^2-x^2)=(x^4-x^2+1)((x^2-x+1)(x^2+x+1)
2)
(a-1)^2 (a+2)=a (a^2-3)+2=(a-1)^3+3 (a-1)^2
3)x^2 (x^2+y^2)+y^4=x^4+y^2 (x^2+y^2)=(x^2-x y+y^2) (x^2+x y+y^2)
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Answers & Comments
=(x^4-x^2+1)((x^2+1)^2-x^2)=(x^4-x^2+1)((x^2-x+1)(x^2+x+1)
2)(a-1)^2 (a+2)=a (a^2-3)+2=(a-1)^3+3 (a-1)^2
3)x^2 (x^2+y^2)+y^4=x^4+y^2 (x^2+y^2)=(x^2-x y+y^2) (x^2+x y+y^2)