Question

2.09 Without actual multiplication evaluate.
252 - 242.​

Answer 1

CORRECT QUESTION -

Without actual multiplication evaluate :

(Ⅰ) 25² - 24²

CORRECT ANSWER -

(Ⅰ) 25² - 24²

= (25 + 4) (25 - 4) [applying a² - b² = (a+b)(a-b)]

= (49) × (1)

= 49

SOME EXPANSIONS -

(Ⅰ) (a + b)² = (a² + b² + 2ab)

(Ⅱ) (a - b)² = (a² + b² - 2ab)

(Ⅲ) (a + b + c)² = (a² + b² + c²) 2(ab+bc+ca)

(Ⅳ) (a + b)³ = a³ + b³ + 3ab(a + b)

(Ⅴ) (a - b)³ = a³ - b³ - 3ab(a - b)

(Ⅵ) (a² - b²) = (a + b) (a - b)