Question

Use (a - b)2 = a - 2ab + b2 to evaluate the following
By using suitable identities, evaluate the following:
(i) (103)^3
(i) (99)^3​

Answer 1

I) 103 = 100 + 3

so, 103^2 = (100 + 3)^2

=> 100^2 +2(100)(3) + 3^2

=> 10000 + 600 + 9

=> 10609.

ii) 99 = 100 -1

so, 99^2 = (100 - 1)^2

=> 100^2 -2(100)(1) + 1^2

=> 10000 - 200 + 1

=> 9801

Please mark it as brainliest.

Answer 2

Given

By using suitable identities, evaluate the following:

(i) (103)^3

(i) (99)^3

Solution

• (103)³

→ (100 + 3)³

★ Apply identity :

(a + b)³ = a³ + b³ + 3ab

→ (100)³ + (3)³ + 3 × 100 × 3 (100 + 3)

→ 1000000 + 27 + 900 × 103

→ 1000027 + 92700

→ 192727

_________________________

• (99)³

→ (100 - 1)³

★ Apply identity :

(a - b)³ = a³ - b³ - 3ab(a - b)

→ (100)³ - (1)³ - 3 × 100 × 1(100 - 1)

→ 1000000 - 1 - 300 × 99

→ 999999 - 29700

→ 970299

Additional Information

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a - b)
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)