Вопрос:

Разложите на множители: 22. -c(-d-3)² 23. a(x-y)²+b(x-y) 24. x(a+1)²-y(a+1)² 25. (x+y)²-x(x+y)³ 26. 4m(n-m)² - 16m²(m-n)

Ответ:

Разложите на множители:

  1. \( -c(-d-3)^2 = -c(d+3)^2 = -c(d^2+6d+9) = -cd^2-6cd-9c \)
  2. \( a(x-y)^2+b(x-y) = (x-y)[a(x-y)+b] = (x-y)(ax-ay+b) \)
  3. \( x(a+1)^2-y(a+1)^2 = (a+1)^2(x-y) \)
  4. \( (x+y)^2-x(x+y)^3 = (x+y)^2[1-x(x+y)] = (x+y)^2(1-x^2-xy) \)
  5. \( 4m(n-m)^2 - 16m^2(m-n) = 4m(n-m)^2 + 16m^2(n-m) = 4m(n-m)[(n-m) + 4m] = 4m(n-m)(n+3m) \)

Ответ: 1. -cd² - 6cd - 9c; 2. (x-y)(ax-ay+b); 3. (a+1)²(x-y); 4. (x+y)²(1-x²-xy); 5. 4m(n-m)(n+3m).