Đáp án+Giải thích các bước giải:

 `A_{2}=x^{4}+x^{2}+1`

`=[(x^{2})^{2}+2.x^{2}.1+1^{2}]+x^{2}-2x^{2}`

`=(x^{2}+1)^{2}-x^{2}`

`=(x^{2}+1-x).(x^{1}+1+x)`

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`A_{3}=x^{4}+64y^{4}`

`=(x^{2})^{2}+2.x^{2}.8y^{2}+(8y^{2})^{2}-2.x^{2}.8y^{2}`

`=(x^{2}+8y^{2})^{2}-16x^{2}y^{2}`

`=(x^{2}+8y^{2})^{2}-(4xy)^{2}`

`=(x^{2}-4xy+8y^{2}).(x^{2}+4xy+8y^{2})`

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`A_{4}=x^{4}+5x^{2}+9`

`=[(x^{2})^{2}+2.x^{2}.3+3^{2}]+5x^{2}-6x^{2}`

`=(x^{2}+3)^{2}-x^{2}`

`=(x^{2}-x+3).(x^{2}+x+3)`

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`A_{5}=a^{3}+b^{3}+c^{3}-3ab`

`=(a^{3}+3a^{2}b+3ab^{2}+b^{3})+c^{3}-3a^{2}b-3ab^{2}-3ab`

`=[(a+b)^{3}+c^{3}]-3ab.(a+b+c)`

`=(a+b+c).[(a+b)^{2}-(a+b).c+c^{2}]-3ab.(a+b+c)`

`=(a+b+c).(a^{2}+2ab+b^{2}-ac-bc+c^{2}-3ab)`

`=(a+b+c).(a^{2}+b^{2}+c^{2}-ab-ac-bc)`