Question

Evaluate: ${\displaystyle (\frac{4}{7}\text{a}+\frac{3}{4}\text{b})(\frac{4}{7}\text{a}-\frac{3}{4}\text{b})}$

Answer 1

${\displaystyle (\frac{4}{7}\text{a}+\frac{3}{4}\text{b})(\frac{4}{7}\text{a}-\frac{3}{4}\text{b})}$

${\displaystyle ={\left(\frac{4}{7}\text{a}\right)}^2-{\left(\frac{3}{4}\text{b}\right)}^2}$  ......[ ∵ (a − b) (a + b) = a²b²]

${\displaystyle =\frac{16}{49}{\text{a}}^2-\frac{9}{16}{\text{b}}^2}$