Question

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

\[x = \frac{- 12}{5}, y = \frac{- 15}{4}, z = \frac{8}{3}\]

Answer 1

\[\text{We have to verify that} x \times (y + z) = x \times y + x \times z . \]
\[x = \frac{- 12}{5}, y = \frac{- 15}{4}, z = \frac{8}{3}\]
\[x \times (y + z) = \frac{- 12}{5} \times (\frac{- 15}{4} + \frac{8}{3}) = \frac{- 12}{5} \times \frac{- 45 + 32}{12} = \frac{- 12}{5} \times \frac{- 13}{12} = \frac{13}{5}\]
\[x \times y + x \times z = \frac{- 12}{5} \times \frac{- 15}{4} + \frac{- 12}{5} \times \frac{8}{3}\]
\[ = \frac{9}{1} + \frac{- 32}{5}\]
\[ = \frac{45 - 32}{5}\]
\[ = \frac{13}{5}\]
\[ \therefore \frac{- 12}{5} \times (\frac{- 15}{4} + \frac{8}{3}) = \frac{- 12}{5} \times \frac{- 15}{4} + \frac{- 12}{5} \times \frac{8}{3}\]
\[\text{Hence verified .} \]