41. Given exp. =[(a + b)² - 4ab], where a =476 and b =424
= [(476 + 424)² - 4 x 476 x 424]
= [(900)² - 8072296 = 810000 – 807296 =2704
42. (112 x 5⁴) = 112 x (10/2)² = 112 x 10⁴/2⁴ = 1120000/16 = 70000.
43. 935421 x 625 = 935421 x 5² = 935421 x (10/2)²
935421 x 10⁴ = 9354210000
2⁴ 16
= 584638125.
44. 12345679 x 72= 12345679 x (70 + 2)
= 12345679 x 70 + 123455679 x 2
= 864197530 + 24691358 864197530
=888888888 24691358
888888888
45. Given exp. = (397)² + (104)² + 2 x 397 x 104
= (397 + 104)² = (501)² = (500 + 1)²
= (500)² + 1² + 2 x 500 x 1 = 250000 +1 + 1000
= 251001
46. 20 x X = (64 +36) (64 – 36) = 100 x 28
X = 100 x 28 = 140.
20
47.Given exp. = ( a + b)² - (a – b)² = 4ab =4
ab ab
48.
Given exp. (a + b) ² + ( a –b )² = 2 (a² + b²) =2
Given exp. (a + b) ² + ( a –b )² = 2 (a² + b²) =2
(a² + b²) (a² + b²
49.
Given exp. (a³ + b³) (a + b) = (768 +232) = 1000.
Given exp. (a³ + b³) (a + b) = (768 +232) = 1000.
(a² -ab + b²)
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