Question

If a = -25, b = 20 cm and c = -10, verify that:
(i) a + (b + c) = (a + b) + c
(ii) a × (b + c) = a × b + a × c

Answer 1

Given :

• a = -25
• b = 20
• c = -10

To Verify :

• (i) a + (b + c) = (a + b) + c
• (ii) a × (b + c) = a × b + a × c

Solution :

(i) a + (b + c) = (a + b) + c

Putting Values :

$\longmapsto\tt{-25+(20+(-10)=(-25+20)+(-10)}$

$\longmapsto\tt{-25+(20-10)=-5-10}$

$\longmapsto\tt{-25+10=-5-10}$

$\longmapsto\tt\bf{-15=-15}$

Hence Verified

(ii) a × (b + c) = a × b + a × c

Putting Values :

$\longmapsto\tt{-25\times{(20+(-10)}=-25\times{20}+(-25)\times{-10}}$

$\longmapsto\tt{-25\times{(20-10}=-25\times{20}+(-25)\times{-10}}$

$\longmapsto\tt{-25\times{10}=-25\times{20}+250}$

$\longmapsto\tt{-250=-500+250}$

$\longmapsto\tt\bf{-250=-250}$

Hence Verified

Answer 2

Given :-

a = -25

b = 20

c = 10

To Find :-

(i) a + (b + c) = (a + b) + c

(ii) a × (b + c) = a × b + a × c

Solution :-

(i) a + (b + c) = (a + b) + c

Taking LHS

a + (b + c)

-25 + [20 + (-10)]

-25 + [20 - 10]

-25 + 10

-15

Taking RHS

(a + b) + c

[(-25) + 20] + (-10)

[-25 + 20] - 10

-5 - 10

-15

Hence, Proved

(ii)  a × (b + c) = a × b + a × c

Taking LHS

-25 × [20 + (-10)]

-25 × [20 - 10]

-25 × 10

-250

Taking RHS

[(-25) × 20] + [(-25) × (-10)]

-500 + (250)

-500 + 250

-250

Hence, Proved