1. a) 101² - 99² = (101 + 99)(101 - 99) = 200 . 2 = 400

b) 98.102 = (100 - 2)(100 + 2) = 100² - 4 = 10000 - 4 = 9996

c) 77² + 23² + 77.46 = 77² + 23² + 77.23.2 = (23 + 77)² = 100² = 10000

d) M = x³ + 9x² + 27x + 27 = (x + 3)³ = (7 + 3)³ = 10³ = 1000

2. a) 2x² + 3x - 5 = 0

=> 2x² + 5x - 2x - 5 = 0

=> x(2x + 5) - (2x + 5) = 0

=> (x - 1)(2x + 5) = 0

=> \(\backslash\text{orbr} \left{\right. x - 1 = 0 \\ 2 x + 5 = 0\)

=> \(\backslash\text{orbr} \left{\right. x = 1 \\ x = - \frac{5}{2}\)

b) 2x² - 11x - 51 = 0

=> 2x² - 17x + 6x - 51 = 0

=> x(2x - 17) + 3(2x - 17) = 0

=> (x + 3)(2x - 17) = 0

=> \(\backslash\text{orbr} \left{\right. x + 3 = 0 \\ 2 x - 17 = 0\)

=> \(\backslash\text{orbr} \left{\right. x = - 3 \\ x = \frac{17}{2}\)