Question

Verify the property x*(y+z)=x*y+x*z by taking
1.x= -3/7 y=2/5 z =-4/9

please answer​

Answer 1

$given \: \\ x = \frac{ - 3}{5} \\ y = \frac{2}{5} \: \: \: and \\ z = \frac{ - 4}{9} \\ x(y + z) = xy + xz \\ l.h.s = x(y + z) \\ \: \: \: \: \: \: \: \: \: \: = \frac{ - 3}{5} ( \frac{2}{5} + (\frac{ - 4}{9} )) \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{ - 3}{5} ( \frac{2}{5} - \frac{4}{9} ) \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{ - 3}{5} ( \frac{18 - 20}{45} ) \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{ - 3}{5} ( \frac{ - 2}{45} ) \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{6}{225} \\ \\ r.h.s = xy + xz \\ \: \: \: \: \: \: \: \: \: \: = ( \frac{ - 3}{5} )( \frac{2}{5}) + ( \frac{ - 3}{5} )( \frac{ - 4}{9} ) \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{ - 6}{25} + \frac{12}{45} \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{ - 54 + 60}{225} \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{6}{225} \\ \\ so....l.h.s = r.h.s \: \\ hence \: proved$

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