Question

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

\[x = \frac{- 3}{4}, y = \frac{- 5}{2}, z = \frac{7}{6}\]

Answer 1

\[\text{We have to verify that} x \times (y + z) = x \times y + x \times z . \]
\[ x = \frac{- 3}{4}, y = \frac{- 5}{2}, z = \frac{7}{6}\]
\[x \times (y + z) = \frac{- 3}{4} \times (\frac{- 5}{2} + \frac{7}{6}) = \frac{- 3}{4} \times \frac{- 15 + 7}{6} = \frac{- 3}{4} \times \frac{- 8}{6} = 1\]
\[x \times y + x \times z = \frac{- 3}{4} \times \frac{- 5}{2} + \frac{- 3}{4} \times \frac{7}{6}\]
\[ = \frac{15}{8} + \frac{- 7}{8}\]
\[ = \frac{15 - 7}{8}\]
\[ = 1\]
\[ \therefore \frac{- 3}{4} \times (\frac{- 5}{2} + \frac{7}{6}) = \frac{- 3}{4} \times \frac{- 5}{2} + \frac{- 3}{4} \times \frac{7}{6}\]
\[\text{Hence verified .}\]