Question

Разложи множители на каждый многочлен

Answer 1

1. $11m - 11n + mx - nx = (11m - 11n) + (mx - nx) = 11(m - n) + x(m - n) = (m - n) \times (11 + x)$
2. $7 a+ 7c - ab - bc = 7(a + c) - b \times (a + c) = (a + c) \times (7 - b)$
3. $12 c- 12 -ac + a = 12(c - 1) - a \times (c - 1) = (c - 1) \times (12 - a)$
4. $xy + 9y - x - 9 = y \times (x + 9) - (x + 9) = (x + 9) \times (y - 1)$
5. $3ab + 6a + 7b + 14 = 3a \times (b + 2) + 7(b + 2) = (b + 2) \times (3a + 7)$
6. ${x}^{3} + {x}^{2} - x - 1 = {x}^{2} \times (x + 1) - (x + 1) = (x + 1) \times ( {x}^{2} - 1) = (x + 1) \times (x - 1) \times (x + 1) = (x + 1 {)}^{2} \times (x - 1)$
7. $ab {}^{2} - 3c {}^{2} + b {}^{2} c - 3ac = ab {}^{2} + b {}^{2} c - 3c {}^{2} - 3ac = b {}^{2} \times (a + c) - 3c \times (c + a) = (a + c) \times (b {}^{2} - 3c)$
8. $ab {}^{2} + 7c {}^{2} - abc - 7bc = ab \times (b - c) - 7c \times ( - c + b) = (b - c) \times (ab - 7c)$
9. $17x {y}^{2} - 12y {z}^{2} - 34x {z}^{2} + 6 {y}^{3} = 17 \times ( {y}^{2} - 2 {2}^{2} ) + 6y \times ( - 2 {z}^{2} + {y}^{2} ) = ( {y}^{2} - 2 {z}^{2} ) \times (17x + 6y)$