Question

Verify the property: x × (y + z) = x × y + x × z by taking:

\[x = \frac{- 8}{3}, y = \frac{5}{6}, z = \frac{- 13}{12}\]

Answer 1

\[\text{We have to verify that} x \times (y + z) = x \times y + x \times z . \]
\[x = \frac{- 8}{3}, y = \frac{5}{6}, z = \frac{- 13}{12}\]
\[x \times (y + z) = \frac{- 8}{3} \times (\frac{5}{6} + \frac{- 13}{12}) = \frac{- 8}{3} \times \frac{10 - 13}{12} = \frac{- 8}{3} \times \frac{- 3}{12} = \frac{2}{3}\]
\[x \times y + x \times z = \frac{- 8}{3} \times \frac{5}{6} + \frac{- 8}{3} \times \frac{- 13}{12}\]
\[ = \frac{- 20}{9} + \frac{26}{9}\]
\[ = \frac{- 20 + 26}{9}\]
\[ = \frac{2}{3}\]
\[ \therefore \frac{- 8}{3} \times (\frac{5}{6} + \frac{- 13}{12}) = \frac{- 8}{3} \times \frac{5}{6} + \frac{- 8}{3} \times \frac{- 13}{12}\]
\[\text{Hence verified .} \]