(a) 26 × (-48) + (-48) × (-36)
= 26 × (-48)+ (-36) × (-48)
= [26 + (-36)] × (-48)
∵ Distributive Property = (-10) × (-48)
= + 480
(b) 8 × 53 × (-125)
= 8 × (-125) × 53
= [8 × (-125)] × 53
= [-(8 × 125)] × 53
∵ a × (-b) = -(a × b)
= (-1000) × 53 = -(1000 x 53)
∵ (-a) × (b) = -(a × b) = -53000
(c) 15 × (-25) × (-4) × (-10)
= 15 × (-25) × (-10) × (-4)
∵ commutativity of multiplication
= 15 × (-10) × (-25) × (-4)
= [15 × (-10)] × [(-25) × (-4)]
= [-(15 × 10)] × [25 × 4] (∵ a × (-b)
= -(a × b) = -150 × 100
(-a) × (-b) = a × b = -15000
(d) (-41) × 102 = -(41 × 102)
∵ (-a) × b = -(a × b) =-[41 × (100 + 2)]
= -[41 × 100 + 41 × 2]
Distributivity of multiplication over addition.
= -[4100 + 82] = -4182
(e) 625 × (-35) + (-625) × 65
= 625 × (-35) + 625 × (-65)
∵ (-a) × b = a × (-b)
= 625 × [(-35) + (-65)]
∵ Distributivity of multiplication over addition
= 625 × (-100) = -(625 × 100)
(f) 7 × (50 – 2)
= 7 × 50 – 7 × 2
∵ Distributivity of multiplication over subtraction
= 350 – 14 = 336
(g) (-17) × (-29)
= 17 × 29 ( ∵ (-a) × (-b) = a × b)
= 17 × (30 – 1)
= 17 × 30 – 17 × 1
∴ Distributivity of multiplication over subtraction
= 510 – 17 = 493
(h) (-57) × (-19) + 57
= 57 × 19 + 57
∵ (-a) × (-b) = a × b = 57 × 19 + 57 × 1
∵ (a × 1 = a)
= 57 × (19 + 1)
∴ Distributivity of multiplication over subtraction.
= 57 × 20 = 1140
