Question

Factorise: ${\displaystyle {\left(6\frac{2}{3}\right)}^2-{\left(2\frac{1}{3}\right)}^2}$

Answer 1

${\displaystyle {\left(6\frac{2}{3}\right)}^2-{\left(2\frac{1}{3}\right)}^2}$

${\displaystyle ={\left(\frac{20}{3}\right)}^2-{\left(\frac{7}{3}\right)}^2}$

${\displaystyle =(\frac{20}{3}+\frac{7}{3})(\frac{20}{3}-\frac{7}{3})}$

${\displaystyle =\left(\frac{27}{3}\right)\left(\frac{13}{3}\right)=9\times \frac{13}{3}=39}$