Q.5 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) 26 × (-48) + (-48) × (-36)
= -48 × [26 + (-36)] = -48 × [26 – 36] = -48 × -10 = 480
[Distributive property of multiplication over addition]

(b) 8 × 53 × (-125) = 53 × [8 × (-125)]
[Associative property of multiplication] = 53 × (-1000) = -53000

(c) 15 × (-25) × (-4) × (-10)
= [(-25) × (-4)] × [15 × (-10)]
[Regrouping the terms] = 100 × (-150) = -15000

(d) (-41) × 102 = (-41) × [100 + 2]
= (-41) × 100 + (-41) × 2
[Distributive property of multiplication over addition] = -4100 – 82 = -4182

(e) 625 × (-35) + (-625) × 65
= 625 × [(-35) + (-65)]
[Distributive property of multiplication over addition] = 625 × (-100) = -62500

(f)7 × (50 – 2) = 7 × 50 -7 × 2 = 350 – 14 = 336
[Distributive property of multiplication over addition]

(g) (-17) × (-29) = (-17) × [30 + (-1)]
= (-17) × 30 + (-17) × (-1)= -510 + 17 = -493
[Distributive property of multiplication over addition]

(h) (-57) × (-19) + 57 = 57 × 19 + 57
= 57 × 19 + 57 × 1[Distributive property of multiplication over addition]
= 57 × (19 + 1) = 57 × 20 = 1140