Find the product, using suitable properties:

(a) 26 × (– 48) + (– 48) × (–36)

(b) 8 × 53 × (–125)

(c) 15 × (–25) × (– 4) × (–10)

(d) (– 41) × 102

(e) 625 × (–35) + (– 625) × 65

(f) 7 × (50 – 2)

(g) (–17) × (–29)

(h) (–57) × (–19) + 57

(a) We have,

26 × (-48) + (-48) × (-36)

We know that,

(b × a = a × b)

Also,

(a × b + a × c) = a (b + c)

Therefore,

= (-48) × 26 + (-48) × (-36)

= (-48) [26 + (-36)]

= (-48) [26 – 36]

= (-48) [-10]

= 480

(b) We have,

8 × 53 × (-125)

We know that,

(b × a = a × b)

Also,

a × (b × c) = (a × b) × c

Therefore,

= 8 × [53 × (-125)]

= 8 × [(-125) × 53]

= [8 × (-125)] × 53

= [-1000] × 53

= [-1000] × 53

= - 53000

(c) We have,

15 × (-25) × (-4) × (-10)

Therefore,

= 15 × [(-25) × (-4)] × (-10)

= 15 × (1000) × (-10)

= 15 × (-1000)

= -15000

(d) We have,

(-41) × 102

We know that,

a × (b + c) = (a × b) + (a × c)

Therefore,

= (-41) × (100 + 2)

= (-41) × 100 + (-41) × 2

= - 4100 – 82

= - 4182

(e) We have,

625 × (-35) + (-625) × 65

We know that,

(a × b + a × c) = a (b + c)

Therefore,

= 625 × [(-35) + (-65)]

= 625 × [-100]

= - 62500

(f) We have,

7 × (50 - 2)

We know that,

a × (b – c) = (a × b)- (a × c)

Therefore,

= (7 × 50) – (7 × 2)

= 350 – 14

= 336

(g) We have,

(-17) × (-29)

We know that,

a × (b + c) = (a × b)+ (a × c)

Therefore,

= (-17) × [-30 + 1]

= [(-17) × (-30)] + [(-17) × 1]

= [510] + [-17]

= 493

(h) We have,

(-57) × (-19) + 57

We know that,

(a × b) + (a × c) = a × (b + c)

Therefore,

= 57 × 19 + 57 × 1

= 57 [19 + 1]

= 57 × 20

= 1140

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