Ex 1 :

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1) R = 8/3 - 5/3 : 20/21 = 8/3 - 5/3 × 21/20 = 8/3 - 1/1 × 7/4 = 8/3 - 7/4 = 32/12 - 21/12 = 11/12

2) A = 2√45 - √125 + 3√80 = 2√(9 × 5) - √(25 × 5) + 3√(16 × 5) =  2 × 3√5 - 5√5 + 3 × 4√5 = (6 - 5 + 12)√5 = 13√5

B = 5√20 × √45 × √5 = 5√(20 × 45 × 5) = 5√(4 × 5 × 9 × 5 × 5) = 5 × 2 × 3 × 5√5 = 150√5

3) C = (150 × 10³ × 8 × 10⁵) / (6 × 10⁷) = (15 × 8 × 10⁹) /(3 × 2 × 10⁷) = (5 × 4 × 10⁹) / 10⁷ = 20 × 10⁹⁻⁷ = 20 × 10² = 2 000 = 2 × 10³

Ex. 2 :

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1) E = (5x - 2)² - (x - 7) (5x - 2) = 25x² - 20x + 4 - (5x² - 2x - 35x + 14) = 20x² + 17x - 10

2) E(-1) = 20(-1)² + 17(-1) - 10 = 20 - 17 - 10 = -7

3) E = (5x - 2)² - (x - 7) (5x - 2) = (5x - 2) (5x - 2) - (x - 7) (5x - 2) = (5x - 2)  (5x - 2 - (x - 7)) = (5x - 2)  (4x + 5)