Exercise 1.5

(i)

(i) 18 × [7+(-3)] = [18×7] + [18×(-3)]

Solution:

Solve the left-hand side (LHS)

7 + (−3) =

18 × 4 =

Solve the right-hand side (RHS)

18 × 7 =

18 × (−3) =

126 + (−54) = 126 − 54 =

Compare LHS and RHS 72 = 72

Since both sides are equal, the given equation is verified

(ii)

(ii) (-21) × [(-4) + (-6)] = [(-21) × (-4)] + [(-21) × (-6)]

Solution:

Solve the Left-Hand Side (LHS)

First, simplify the expression inside the brackets:

(−4) +(−6) =

Now, multiply by -21: (−21) × (−10) =

Solve the Right-Hand Side (RHS)

Calculate each term separately:

(−21) × (−4) =

(−21) × (−6) =

Now, sum them: 84 + 126 =

Compare LHS and RHS 210=210

Since both sides are equal, the equation is verified

(i)

(i) 26 × (-48) + (-48) × (-36)

Solution:

Identify the Common Factor

Observing the given expression, we see that is a common factor:

26 × (−48) + (−48) × (−36)

Using the distributive property:

a × c + b × c =(a+b) × c

Here, a = , b = and c = .

Apply the Distributive Property

(26+(−36)) × (−48)

Simplify inside the parentheses:

(26−36) × (−48) = (−10) × (−48)

Multiply

(−10) × (−48) =

(ii)

(ii) 625 × (-35) + (-625) × 65

Solution:

Observing the given expression, we see that 625 is a common factor:

625 × (−35) + (−625) × 65

Rewriting:

625 × (−35) + (−1) × 625 × 65

Since is also a factor in the second term, we rewrite:

625 × (−35) −625 × 65

Now, applying the distributive property:

a × c + b × c =(a+b) × c

Here, a = , b = , and c = .

Apply the Distributive Property

(−35+(−65)) × 625

Simplify inside the parentheses:

(−35−65) × 625 = (−100) × 625

Multiply

−100 × 625 = −62500-65499