Question

Verify that a× (b + c) = (a × b) + (a × c) : a= -4/5 ; b= -6/7 ; c= -2/3

Answer 1

Given:

$a = - \frac{4}{5}$

$b = - \frac{6}{7}$

$c = - \frac{2}{3}$

To verify:

a×(b+c) = (a×b) + (a×c)

Solution:

PROPERTY USED → Distributive Property

⇒ A(B+C) = AB + BC

We will simplify both the sides separately

LHS = a × (b + c)

$= > - \frac{4}{5} \times \left( - \frac{6}{7} + ( - \frac{2}{3}) \right)$

$= > - \frac{4}{5} \times \left( - \frac{6}{7} - \frac{2}{3} \right)$

$= > - \frac{4}{5} \times \left( \frac{ - 6(3) - 2(7)}{21} \right)$

$= > - \frac{4}{5} \times \left( \frac{ - 18 - 14}{21} \right)$

$= > - \frac{4}{5} \times \left( - \frac{32}{21} \right)$

$= \boxed{\frac{128}{105} }$

RHS = (a × b) + (a × c)

$= > \left[- \frac{4}{5} \times (- \frac{6}{7} ) \right] + \left[ - \frac{4}{5} \times ( - \frac{2}{3}) \right ]$

$= > \frac{24}{35} + \frac{8}{15}$

Taking LCM

$= > \frac{72 + 56}{105}$

$= \boxed{ \frac{128}{105}}$

LHS = RHS

Hence verified!!