Factorise : a^2 + 1/a^2 + 3 -2a - 2/a

Question

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

Answer 1

(d) \(\big(a+\frac1a-1\big)^2\)

\(a^2 + \frac1{a^2}+3-2a-\frac2a\) 

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

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

= \(\big(a+\frac1a-1\big)^2\)