Evaluate the following, using distributive property.

(i) –39 × 99

(ii) (– 85) × 43 + 43 × (– 15)

(iii) 53 × (– 9) – (– 109) × 53

(iv) 68 × (–17) + ( –68) × 3

In distributive property, numbers are split in such a way that it becomes easy to evaluate them after splitting.

(i). -39 × 99

We can write it as,

99 × -39 = (100 – 1) × (-39) [∵ 100 – 1 = 99]

⇒ 99 × -39 = [100 × (-39)] – [1 × (-39)] [∵ (a – b) × c = ac – bc]

⇒ 99 × -39 = -3900 – (-39)

⇒ 99 × -39 = -3900 + 39

⇒ 99 × -39 = -3861

Thus, the answer is -3861.

(ii). (-85) × 43 + 43 × (-15)

We can write it as,

(-85) × 43 + 43 × (-15) = 43 × (-85 + (-15)) [Taking 43 common]

⇒ (-85) × 43 + 43 × (-15) = 43 × (-85 – 15) [plus & minus = minus]

⇒ (-85) × 43 + 43 × (-15) = 43 × -100

⇒ (-85) × 43 + 43 × (-15) = -4300

Thus, the answer is -4300.

(iii). 53 × (-9) – (-109) × 53

We can write it as,

53 × (-9) – (-109) × 53 = 53 × (-9 – (-109)) [Taking 53 common]

⇒ 53 × (-9) – (-109) × 53 = 53 × (-9 + 109) [minus & minus = plus]

⇒ 53 × (-9) – (-109) × 53 = 53 × 100

⇒ 53 × (-9) – (-109) × 53 = 5300

Thus, the answer is 5300.

(iv). 68 × (-17) + (-68) × 3

We can write it as,

68 × (-17) + (-68) × 3 = 68 × (-17) – 68 × 3 [minus & plus = minus]

⇒ 68 × (-17) + (-68) × 3 = 68 × (-17 – 3) [Taking 68 as common]

⇒ 68 × (-17) + (-68) × 3 = 68 × (-20)

⇒ 68 × (-17) + (-68) × 3 = -1360

Thus, the answer is -1360.