Question

using (a-b)(a+b) = a^2 - b^2 expand (x- y/5 -1)(x+ y/5 +1)

Answer 1

$\huge\mathfrak{\underline{\overline{Answer}}}$

$( \frac{x - y}{5} - 1)( \frac{x + y}{5} + 1)$

$( \frac{x - y - 5}{5} )( \frac{x + y + 5}{5} ) \\ = ( \frac{x - (y + 5)}{5} )( \frac{x + (y + 5)}{5} ) \\ = ( \frac{x}{5} - \frac{y + 5}{5} )( \frac{x}{5} + \frac{y + 5}{5} ) \\ = ({ \frac{x}{5} )}^{2} - ( { \frac{y + 5}{5}) }^{2} \\ = \frac{ {x}^{2} }{ {5}^{2} } - \frac{ {(y + 5)}^{2} }{ {5}^{2} } \\ = \frac{ {x}^{2} }{25} - \frac{ {y}^{2} + 10y + 25}{25} \\ = \frac{ {x}^{2} - {y}^{2} - 10y - 25 }{25}$