Question

Use the formula to find the values of the following:

(1) 53³
(2) 102³
(3) 44³
(4) 61³
(5) 104³
(6) 301³
(7) 505³

Answer 1

(1) 53³ = (50 + 3)³
or 53³ = 50³ + 3³ + 3 × (50)² ×(3) + 3 × (50) × (3)²
= 125000 + 27 + 22500 + 1350
= 148877

(2) 102³ = (100 + 2)³
or 102³ = 100³ + 2³ + 3 × (100)² × (2) + 3 × (100) × (2)²
= 1000000 + 8 + 60000 + 1200
= 1061208

(3) 44³ = (40 + 4)²
or 44³ = 40³ + 4³ + 3 × (40)² × (4) + 3 × (40) × (4)²
= 64000 + 64 + 19200 + 1920
= 85184

(4) 61³ = (60 + 1)³
or 61³ = 60³ + 1³ + 3 × (60)² × (1) + 3 × (60) × (1)²
= 216000 + 1 + 10800 + 180
= 226981

(5) 104³ = (100 + 4)³
or 104³ = 100³ + 4³ + 3 × (100)² × (4) + 3 × (100) × (4)²
= 1000000 + 64 + 120000 + 4800
= 1124864

(6) 301³ = (300 + 1)³
or 301³ = 300³ + 1³ + 3 × (300)² × (1) + 3 × (300) ×(1)²
= 27000000 + 1+ 270000 + 900
= 27270901

(7) 505³ = (500 + 5)³
or 505³ = 500³ + 5³ + 3 × (500)² × (5) + 3 × (500) × (5)²
= 125000000 + 125 + 3750000 + 37500
= 128787625