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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