Question

a4 + a2 + 1 . Factorise it.

Answer 1

a(a2)2+2a2+1-a2
(a2+1)2-a2
(a2+1)2-(a)2
(a2+1-a)(a2+1+a)
(a2-a+1)(a2+a+1) ans

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Answer 2

Answer:

$Factors \: of \: a^{4}+a^{2}+1\\=(a+1+\sqrt{a})(a+1-\sqrt{a})(a^{2}-a+1)$

Step-by-step explanation:

$Given \:expression a^{4}+a^{2}+1\\=(a^{4}+2a^{2}+1)-a^{2}\\=[(a^{2})^{2}+2\times a^{2}\times 1+1^{2}]-a^{2}\\=(a^{2}+1)^{2}-a^{2}$

$=(a^{2}+1+a)(a^{2}+1-a)$

/* By algebraic identity:

x²-y²=(x+y)(x-y) */

$=(a^{2}+2a+1-a)(a^{2}+1-a)$

$=[(a^{2}+2\times a\times 1+1)-(\sqrt{a}^{2})](a^{2}+1-a)$

$=[(a+1)^{2}-(\sqrt{a})^{2}](a^{2}-a+1)$

$=(a+1+\sqrt{a})(a+1-\sqrt{a})(a^{2}-a+1)$

Therefore,

$Factors \: of \: a^{4}+a^{2}+1\\=(a+1+\sqrt{a})(a+1-\sqrt{a})(a^{2}-a+1)$

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