Question

Simplify:
(i) (−9) × 6 + (−9) × 4
(ii) 8 × (−12) + 7 × (−12)
(iii) 30 × (−22) + 30 × (14)
(iv) (−15) × (−14) + (−15) × (−6)
(v) 43 × (−33) + 43 × (−17)
(vi) (−36) × (72) + (−36) × 28
(vii) (−27) × (−16) + (−27) × (−14)

Answer 1

(i) (–9) × 6 + (–9) × 4
Solution:
Using the distributive law:
(–9) × 6 + (–9) × 4
= (–9) × (6+9)
= (–9) × 10
= –90

(ii) 8 × (–12) + 7 × (–12)
Solution:
Using the distributive law:
8 × (–12) + 7 × (–12)
= (–12) × (8+7)
= (–12) × 15
= –180

(iii) 30 × (–22) + 30 × (14)
Solution:
Using the distributive law:
30 × (–22) + 30 × (14)
= 30 × [(–22) + 14]
= 30 × [–22 + 14]
= 30 × (–8)
= –240

(iv) (–15) × (–14) + (–15) × (–6)
Solution:
(–15) × (–14) + (–15) × (–6)
Using the distributive law:
= (–15) × [ (–14) + (–6)]
= (–15) × [–14 – 6]
= (–15) × (–20)
= 300

(v) 43 × (–33) + 43 × (–17)
Solution:
43 × (–33) + 43 × (–17)
Using the distributive law:
= (43 ) × [–(33) + (–17)]
= (43 ) × [–33 – 17]
= 43 × (–50)
= –2150

(vi) (–36) × (72) + (–36) × 28
Solution
(–36) × (72) + (–36) × 28
Using the distributive law:
= (–36) × (72 + 28 )
= (–36) × 100
= –3600

(vii) (–27) × (–16) + (–27) × (–14)
Solution:
(–27) × (–16) + (–27) × (–14)
Using the distributive law:
= (–27) × [(–16) + (–14)]
= (–27) × [–16 –14]
= (–27) × [–30]
= 810