Разложите на множителиa) 5a-5b+c (a-b); б) a³-a²-4a+4; в) 25b² - (b-5) ²

a) 5a - 5b + c (a - b) = 5 (a - b) + c (a - b) = (a - b) (5 + c);

б) a³ - a² - 4a + 4 = a² (a - 1) - 4a + 4 = a² (a - 1) - 4 (a - 1) = (a - 1) (a² - 4) = (a - 1) (a² - 2²) = (a - 1) (a - 2) (a + 2);

в) 1 способ: 25b² - (b - 5) ² = (5b) ² - (b - 5) ² = (5b - (b - 5)) (5b + (b - 5)) = (5b - b + 5) (5b + b - 5) = (4b + 5) (6b - 5).

2 способ: 25b² - (b² - 10b + 25) = 25b² - b² + 10b - 25 = 24b² + 10b - 25.

Приравниваем к нулю и находим решение:

24b² + 10b - 25 = 0;

D = 100 - 4 * 24 * ( - 25) = 100 + 2400 = 2500>0;

b₁ = ( - 10 - 50) / 48 = - 60/48 = - 20/16 = - 5/4 = - 1 1/4;

b₂ = ( - 10 + 50) / 48 = 40/48 = 20/24 = 5/6.

24b² + 10b - 25 = 24 (b + 1 1/4) (b - 5/6).