5. 16х² + 40хb³ + 25b⁶ = 4²x² + 2·4x·5b³ + 5²b⁶ = (4x +5b³)²
(9 - a²)a² - 2a(9 - a²) + 9 - a² = (9 - a²)(a² - 2a + 1) = (3 - a)(3 + a)( a - 1)²
6. (x² - 5x) - x + 5 =0;
x(x - 5) - (x -5) = 0;
(x - 5)(x - 1) = 0;
x - 5 = 0 или x - 1 = 0
x = 5, x = 1
7, (3,6·7,6² - 3,6·2,4²)/(1,8·6,5² - 1,8·3,5²) = 3,6·(7,6 + 2,4)(7,6 - 2,4)/(1,8·(6,5 + 3,5)(6,5 - 3,5) = 3,6·10·5,2/1,8·10·3= 10,4/3
8. (ax + by)² + (ay - bx)² = a²x² + 2abxy +b²y² + a²y² - 2abxy + b²x² = a²x² + b²x² + a²y² + b²y² = a²(x² + y²) + b²(x² + y²) = (a² + b²)(x² + b²)
9. (0,4x - y)/(0,8x² - 5y²) = (0,4x - y)/5(0,4x - y)(0,4x +y) = 1/5(0,4x +y) = 1/(2x +5y) = 1/1 = 1