Factorise : a2 + \(\frac1{a^2}\) + 3 -2a - \(\frac2a\)

1.	Factorise : a2 + \(\frac1{a^2}\) + 3 -2a - \(\frac2a\)
Answer» (d) \(\big(a+\frac1a-1\big)^2\) \(a^2 + \frac1{a^2}+3-2a-\frac2a\) = \(a^2 + \frac1{a^2}+1+2-2a-\frac2a\) = \((a)^2+\big(\frac1a\big)^2+(-1)^2+2\times{a}\times\frac1a+2\times{a}\times(-1)+2\times\frac1a\times-1\) = \(\big(a+\frac1a-1\big)^2\)

Answer»

(d) \(\big(a+\frac1a-1\big)^2\)

\(a^2 + \frac1{a^2}+3-2a-\frac2a\)

= \(a^2 + \frac1{a^2}+1+2-2a-\frac2a\)

= \((a)^2+\big(\frac1a\big)^2+(-1)^2+2\times{a}\times\frac1a+2\times{a}\times(-1)+2\times\frac1a\times-1\)

= \(\big(a+\frac1a-1\big)^2\)

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