Question

Use the direct method to evaluate :
${\displaystyle (\frac{3}{5}\text{a}+\frac{1}{2})(\frac{3}{5}\text{a}-\frac{1}{2})}$

Answer 1

Note: (a+b) (a−b) = a² − b²

${\displaystyle (\frac{3}{5}\text{a}+\frac{1}{2})(\frac{3}{5}\text{a}-\frac{1}{2})}$

${\displaystyle ={\left(\frac{3}{5}\text{a}\right)}^2-{\left(\frac{1}{2}\right)}^2}$

${\displaystyle =\frac{9}{25}{\text{a}}^2-\frac{1}{4}}$