Question

Using formula (a‐b)² =(a²‐2ab+b²)

i . (196)²
ii . (689)²​

Answer 1

Solution:

$i. (196)²$

$=>(200-4)²$

$=>(200)²-2×200×4+(4)²$

$=>40000-1600+16$

$=>40016-1600$

$=>38,416$

$ii. (689)²$

$=>(690-1)²$

$=>(690)²-2×690×1+(1)²$

$=>476100-1380+1$

$=>476101-1380$

$=>474,721$

Answer 2

Given :-

• (196)²
• (689)²

Solution :-

→ (196)²

→ (200 - 4)²

• Apply identity
• (a - b)² = a² + b² - 2ab

→ (200)² + (4)² - 2 × 200 × 4

→ 40000 + 16 - 1600

→ 40016 - 1600

→ 38416

________________________________

→ (689)²

→ (700 - 11)²

→ (700)² + (11)² - 2 × 700 × 11

→ 490000 + 121 - 15400

→ 490121 - 15400

→ 474721

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Some Identities :-

• (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)
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)