Question

Verify the property X x (Y + Z ) = ( X x Y ) + ( X x Z) by using:- X = −2/3 , Y = −4/6 , Z = −7/19
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Answer 1

Distributive property ...

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Answer 2

Given X = −2/3 , X = −4/6 , Z = −7/19

Let,

• LHS = X × (Y + Z )
• RHS = ( X × Y ) + ( X × Z)

On Solving LHS,

${ \sf\: \: \: \: \: \mapsto \: \: X × (Y + Z )}$

• Putting the values

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{ - 2}{3} × \bigg ( \dfrac{ - 4}{6} + \dfrac{ - 7}{6} \bigg )}$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{ - 2}{3} × \bigg ( \dfrac{ - 76 - 42}{114} \bigg )}$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{ - 2}{3} × \dfrac{ - 118}{114} }$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{236}{342} }$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{ 118}{171} }$

On Solving RHS

${ \sf\: \: \: \: \: \mapsto \: \: ( X × Y ) + ( X × Z)}$

• Putting the values

${ \sf\: \: \: \: \: \mapsto \: \: \bigg( \dfrac{ - 2}{3} \times \dfrac{ - 4}{6} \bigg ) +\bigg ( \dfrac{ - 2}{3} \times \dfrac{ - 7}{14}\bigg )}$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{8}{18} + \dfrac{14}{57}}$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{456 + 252}{1026} }$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{708}{1026} }$

${ \sf\: \: \: \: \: \mapsto \: \: \dfrac{118}{171} }$

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: LSH = RHS _{_{_{_{\bf Verified}}}}}$