Question

pls fast it's urgent

correct answer pls....​

Answer 1

$\bf{ \underline{ \underline{R equired \: E xplanation..}}}$

Given to verify that :-

a × ( b + c ) = ( a × b ) + ( a× c) where,

• a = -15/4
• b = 4/7
• c = -12/5

Take the L.H.S :-

a × ( b + c ) =

$\rm \: \dfrac{ - 15}{4} \times \bigg( \dfrac{4}{7} - \dfrac{12}{5} \bigg)$

L.C.M of 7,5 is 35 .

$\longrightarrow \rm \: \dfrac{ - 15}{4} \times \bigg( \dfrac{4 \times 5 - 12 \times 7}{35} \bigg)$

$\longrightarrow \rm \: \dfrac{ - 15}{4} \times \bigg( \dfrac{20 - 84}{35} \bigg)$

$\longrightarrow \rm \: \dfrac{ - 15}{4} \times \bigg( \dfrac{ - 64}{35} \bigg)$

$\longrightarrow \bigg( \rm \: \dfrac{ - 15 \times - 64}{4 \times 35} \bigg)$

$\longrightarrow \bigg( \rm \: \dfrac{ 15 \times 64}{4 \times 35} \bigg)$

$\longrightarrow \bigg( \rm \: \dfrac{ 15 \times 16}{ 35} \bigg)$

$\longrightarrow \bigg( \rm \: \dfrac{ 3 \times 16}{ 7} \bigg)$

$\longrightarrow \bigg( \rm \: \dfrac{ 48}{ 7} \bigg)$

L.H.S = 48/7

___________________...

Take R.H.S:-

( a × b ) + (a ×c )

$\longrightarrow \bigg( \rm \dfrac{ - 15}{4} \times \dfrac{4}{7} \bigg) + \bigg( \dfrac{ - 15}{4} \times \dfrac{ - 12}{5} \bigg)$

$\longrightarrow \bigg( \rm \dfrac{ - 15}{ \not4} \times \dfrac{ \not4}{7} \bigg) + \bigg( \dfrac{ \not- 15}{ \not4} \times \dfrac{ \not - 12}{ \not5} \bigg)$

$\longrightarrow \bigg( \rm\dfrac{ - 15}{7} \bigg) + \bigg( 3 \times3 \bigg)$

$\longrightarrow \bigg( \rm\dfrac{ - 15}{7} \bigg) + \bigg( 9 \bigg)$

$\longrightarrow \bigg( \rm\dfrac{ - 15 + 63}{7} \bigg)$

$\longrightarrow \bigg( \rm\dfrac{ 48 }{7} \bigg)$

So,

R.H.S =48/7

__________________...

L.H.S = R.H.S = 48/7

Hence verified!