riza los siguientes polinomios. \( (y+1)-3(y+1) \) \( (b-1)+c(b-1) \) \( \left.d w^{2}-a^{2}\right)+2\left(w^{2}-a^{2}\right) \) \( m(a-c)+a-c \) \( b(a+1)-a-1 \) \( 1-b+2 a(1-b) \) \( (a+2)(a+1)-4(a+1) \) \( \dot{m}(n-2)+2-n \) \( (1+3 n)(m+1)-2 n(m+1)+3(m+1) \) \( d(x-3 y)+d(3 y-x) \)

Vamos a simplificar los polinomios uno por uno. 1. \( (y+1)-3(y+1) \) \[ = (y + 1) - 3(y + 1) = (y + 1) - 3y - 3 = -2y - 2 \] 2. \( (b-1)+c(b-1) \) \[ = (b - 1) + c(b - 1) = (b - 1) + cb - c = (1 + c)b - (1 + c) \] 3. \( \left.d w^{2}-a^{2}\right)+2\left(w^{2}-a^{2}\right) \) \[ = (d w^{2} - a^{2}) + 2(w^{2} - a^{2}) = d w^{2} - a^{2} + 2w^{2} - 2a^{2} = (d + 2)w^{2} - 3a^{2} \] 4. \( m(a-c)+a-c \) \[ = m(a - c) + a - c = ma - mc + a - c = (m + 1)a - (m + 1)c \] 5. \( b(a+1)-a-1 \) \[ = b(a + 1) - a - 1 = ba + b - a - 1 = (b - 1)a + (b - 1) \] 6. \( 1-b+2 a(1-b) \) \[ = 1 - b + 2a(1 - b) = 1 - b + 2a - 2ab = (2a + 1 - b - 2ab) \] 7. \( (a+2)(a+1)-4(a+1) \) \[ = (a + 2)(a + 1) - 4(a + 1) = (a^2 + 3a + 2) - (4a + 4) = a^2 - a - 2 \] 8. \( \dot{m}(n-2)+2-n \) \[ = \dot{m}(n - 2) + 2 - n = \dot{m}n - 2\dot{m} + 2 - n = (\dot{m} - 1)n + (2 - 2\dot{m}) \] 9. \( (1+3 n)(m+1)-2 n(m+1)+3(m+1) \) \[ = (1 + 3n)(m + 1) - 2n(m + 1) + 3(m + 1) = (m + 1) + 3n(m + 1) - 2n(m + 1) + 3(m + 1) \] \[ = (m + 1) + (3n - 2n)(m + 1) + 3(m + 1) = (m + 1 + 3(m + 1)) + n(m + 1) = (4 + n)(m + 1) \] 10. \( d(x-3 y)+d(3 y-x) \) \[ = d(x - 3y) + d(3y - x) = dx - 3dy + 3dy - dx = 0 \] Así que los polinomios simplificados son: 1. \( -2y - 2 \) 2. \( (1 + c)b - (1 + c) \) 3. \( (d + 2)w^{2} - 3a^{2} \) 4. \( (m + 1)a - (m + 1)c \) 5. \( (b - 1)a + (b - 1) \) 6. \( (2a + 1 - b - 2ab) \) 7. \( a^2 - a - 2 \) 8. \( (\dot{m} - 1)n + (2 - 2\dot{m}) \) 9. \( (4 + n)(m + 1) \) 10. \( 0 \)