Using the formula (a-b)^2=(a^2-2ab+b^2), evaluate: i》(196)^2 ii》(689)^2
Answers
Answered by
19
GivEn:
- (a - b)² = (a² + b² - 2ab)
To find:
- i》(196)²
- ii》(689)²
Solution:
• let (196)² be (200 - 4)².
Given, Identity - (a - b)² = (a² + b² - 2ab).
Where,
- A = 200
- B = 4
》(196)²
》(200 - 4)²
★ (a - b)² = (a² + b² - 2ab)
》(200)² + (4)² - 2(200)(4)
》40000 + 16 - 1600
》40016 - 1600
》38416
∴ Hence, (196)² = 38416.
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• Let (689)² be (700 - 11)²
Given, Identity - (a - b)² = (a² + b² - 2ab).
Where,
- A = 700
- B = 11
》(689)²
》(700 - 11)²
★ (a - b)² = (a² + b² - 2ab)
》(700)² + (11)² - 2(700)(11)
》490000 + 121 - 15400
》490121 - 15400
》474721
∴ Hence, (689)² = 474721
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⠀⠀⠀⠀⠀⠀》Algebraic identities :
- (a+ b)² = a² + b² + 2ab
- ( a - b )² = a² + b² - 2ab
- ( a + b )² + ( a - b)² = 2a² + 2b²
- ( a + b )² - ( a - b)² = 4ab
- ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca
- a² + b² = ( a + b)² - 2ab
- (a + b )³ = a³ + b³ + 3ab ( a + b)
- ( a - b)³ = a³ - b³ - 3ab ( a - b)
- If a + b + c = 0 then a³ + b³ + c³ = 3abc
Answered by
25
Given:
Using the formula (a-b)^2=(a^2-2ab+b^2), evaluate:
- 196²
- 689²
Solution:
1. 196²
Let 196² be (200 – 4)²
Also Let,
- a = 200
- b = 4
- Hence, 196² = 38416
________________________________________
2. 689².
Let 689² be (700 – 11)²
Also Let,
- a = 700
- b = 11
- Hence, 689² = 474721
________________________________________
Algebric identities:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² – 2ab + b²
- a² – b² = (a + b) (a – b)
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a – b)³ = a³ – 3a²b + 3ab² + b³
- a³ + b³ = (a + b)(a² – ab + b²)
- a³ – b³ = (a – b) (a² + ab + b²)
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