Question

can anyone factorise it step by step?​

Answer 1

Step-by-step explanation:

$\frac{16 {a}^{2} }{25 {b}^{2} } - \frac{ {x}^{2} }{100 {y}^{2} }$

= $\frac{ {4}^{2} {a}^{2} }{ {5}^{2} {b}^{2} } - \frac{ {x}^{2} }{ {10}^{2} {y}^{2} }$

= ${( \frac{4a}{5b} )}^{2} - {( \frac{x}{10y} )}^{2}$

since, ${a}^{2} + {b}^{2} = (a + b)(a - b)$

= $( \frac{4a}{5b} + \frac{x}{10y} )( \frac{4a}{5b} - \frac{x}{10y} )$