Разложить многочлен на множители 1) 4c^3-32; 2) 9x^2-6xy+y^2+12x-4y; 3) m^2+n^2+2mn+2m+2n+1

1) 4c^3 - 32

4c^3 - 32 = 4 (c^3 - 8) = 4 (c^3 - 2^3) = 4 (c^3 - 2^3) = 4 (c - 2) (c^2 + 2c + 4)

Ответ: 4 (c - 2) (c^2 + 2c + 4)

2) 9x^2 - 6xy + y^2 + 12x - 4y

9x^2 - 6xy + y^2 + 12x - 4y = (9x^2 - 6xy + y^2) + (12x - 4y) = (3x - y) ^2 + 4 (3x - y) = (3x - y) ((3x - y) + 4) = (3x - y) (3x - y + 4)

Ответ: (3x - y) (3x - y + 4)

3) m^2 + n^2 + 2mn + 2m + 2n + 1

m^2 + n^2 + 2mn + 2m + 2n + 1 = m^2 + mn + m + n^2 + mn + n + m + n + 1 = (m^2 + mn + m) + (n^2 + mn + n) + (m + n + 1) = m (m + n + 1) + n (m + n + 1) + (m + n + 1) = (m + n + 1) (m + n + 1) = (m + n + 1) ^2

Ответ: (m + n + 1) ^2