Question

Q 3 : - If a = -35, b = 10 cm and c = -5, verify that:
(i) a + (b + c) = (a + b) + c
(ii) a × (b + c) = a × b + a × c

Answer 1

Answer:

Given that, a= -35, b= 10 & c= -5

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

putting the values,

(-35) + [10 + (-5)] = [(-35) + 10] + (-5)

(-35+5) = (-25-5)

-30 = -30  [ LHS = RHS, verified]

(ii) a × (b+c) = a × b + a × c

(-35) × [10 + (-5)] = (-35) × 10 + (-35) × (-5)

(-35 × 5) = -350 + 175

-175 = -175   [LHS = RHS, verified]

hope it helps you !!!!

Step-by-step explanation:

Answer 2

Given:

The value of a, b and c -

• a = - 35
• b = 10
• c = - 5

What To Verify:

We have to verify -

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

How To Verify:

To verify we have to -

• Substitute the values of a, b and c.
• Solve the LHS and RHS separately.
• Check whether the LHS and RHS are equal.
• Then, it is verified or not according.

Solution:

• i. a + (b + c) = (a + b) + c

Substitute the value of a, b and c,

→ -35 + (10 + (- 5)) = ((- 35) + 10) + (- 5)

Solve the LHS,

→ - 35 + (10 + (- 5))

Solve the brackets,

→ - 35 + (10 - 5)

Solve the brackets further,

→ - 35 + 5

Add the values,

→ - 30

Solve the RHS,

→ ((- 35) + 10) + (- 5)

Remove the brackets,

→ (- 35 + 10) - 5

Solve the brackets further,

→ - 25 - 5

Subtract the values,

→ - 30

By inspection we can see that -

→ LHS = RHS

∴ Hence,  verified.

• ii. a × (b + c) = a × b + a × c

Substitute the value of a, b and c,

→ - 35 × (10 + (- 5)) = - 35 × 10 + (- 35) × (- 5)

Solve the LHS,

→ - 35 × (10 + (- 5))

Solve the brackets,

→ - 35 × (10 - 5)

Solve the brackets further,

→ - 35 × 5

Multiply the values,

→ - 175

Solve the RHS,

→ - 35 × 10 + (- 35) × (- 5)

Solve the term: - 35 × 10

→ - 350 + (- 35) × (- 5)

Solve the term: (- 35) × (- 5)

→ - 350 + 175

Add the values,

→ - 175

By inspection we can see that -

→ LHS = RHS

∴ Hence,  verified.