Question

Factorise the following:

${\displaystyle {\text{m}}^2+\frac{1}{{\text{m}}^2}-23}$

Answer 1

${\displaystyle {\text{m}}^2+\frac{1}{{\text{m}}^2}-23}$ = [Add + 2 and – 2 to make – 23 as – 25]

= ${\displaystyle {\text{m}}^2+\frac{1}{{\text{m}}^2}+2-2-23}$

= ${\displaystyle {\text{m}}^2+\frac{1}{{\text{m}}^2}+2-25}$

= ${\displaystyle {\text{m}}^2+\frac{1}{{\text{m}}^2}+2\times \text{m}\times \frac{1}{\text{m}}-5^2}$

= ${\displaystyle {(\text{m}+\frac{1}{\text{m}})}^2-5^2}$

= ${\displaystyle (\text{m}+\frac{1}{\text{m}}+5)(\text{m}+\frac{1}{\text{m}}-5)}$