Question

${\left(7\frac{3}{10}\right)}^2-{\left(2\frac{1}{10}\right)}^2$.

Answer 1

We know that, We can write mixed function as below:

$a\frac{b}{c}=\frac{a.c+b}{c}=a+\frac{b}{c}$

And we know that $(a^2-b^2)=(a+b)(a-b)$

So, ${\left(7\frac{3}{10}\right)}^2-{\left(2\frac{1}{10}\right)}^2$

$=(7\frac{3}{10}+2\frac{1}{10})(7\frac{3}{10}-2\frac{1}{10})$

$=(7+\frac{3}{10}+2+\frac{1}{10})(7+\frac{3}{10}-2-\frac{1}{10})$

$=(9+\frac{4}{10})(5+\frac{2}{10})$

$=\left(9\right)\left(5\right)+\left(9\right)\left(\frac{2}{10}\right)+\left(\frac{4}{10}\right)\left(5\right)+\left(\frac{4}{10}\right)\left(\frac{2}{10}\right)$

$=45+\frac{18}{10}+\frac{20}{10}+\frac{8}{100}$

$=45+\frac{9}{5}+2+\frac{2}{25}$

$=47+\frac{9\left(5\right)+2}{25}$

$=47+\frac{47}{25}$

$=47+(1+\frac{22}{25})$

$=48+\frac{22}{25}$

$=48\frac{22}{25}$