Resposta:
Explicação passo a passo:
a) 6a².3a + 2ab.3a - 8b².3a - 6a².2b - 2ab.2b + 8b².2b =
18a³ + 6a²b - 24ab² - 12a²b - 4ab² + 16b³ =
18a³ + (6a²b - 12a²b) + (- 24ab² - 4ab²) + 16b³ =
18a³ - 6a²b - 28ab² + 16b³.
b) (- 3x⁴ . x² + 2x³.x² - 4x².x² + 2x.x² - x²) + [- 3x⁴ . (-5x) + 2x³.(-5x) - 4x².(-5x) + 2x.(-5x) - (-5x)] + (- 3x⁴ . 3 + 2x³.3 - 4x².3 + 2x.3 - 3) =
(- 3x⁶ + 2x⁵ - 4x⁴ + 2x³ - x²) + (15x⁵ - 10x⁴ + 20x³ - 10x² + 5x) + (- 9x⁴ + 6x³ - 12x² + 6x - 3) =
- 3x⁶ + (2x⁵ + 15x⁵) + (- 4x⁴ - 10x⁴ - 9x⁴) + (2x³ + 20x³ + 6x³) + (- x² - 10x² - 12x²) + (5x + 6x) - 3 =
- 3x⁶ + 17x⁵ - 23x⁴ + 28x³ - 23x² + 11x - 3.
c) [(3/4)m³.2m - (2/5)m²n.2m + (1/3)mn².2m + (1/2)n³.2m] + [(3/4)m³.3n - (2/5)m²n.3n + (1/3)mn².3n + (1/2)n³.3n]=
[(3/2)m⁴ - (4/5)m³n + (2/3)m²n² + mn³] + [(9/4)m³n - (6/5)m²n² + mn³ + (3/2)n⁴]=
(3/2)m⁴ - [(4/5)m³n +(9/4)m³n] + [(2/3)m²n² - (6/5)m²n²] + [mn³ + mn³] + (3/2)n⁴ =
(3/2)m⁴ - [(4/5)m³n +(9/4)m³n] + [(2/3)m²n² - (6/5)m²n²] + [mn³ + mn³] + (3/2)n⁴ =
Obs: (4/5)m³n +(9/4)m³n = mmc(4,5)=20
(16/20)m³n +(45/20)m³n = (61/20)m³n.
(2/3)m²n² - (6/5)m²n² = mmc(3,5)=15
(10/15)m²n² - (18/15)m²n² = - (8/15)m²n².
(3/2)m⁴ - (61/20)m³n - (8/15)m²n² + 2mn³ + (3/2)n⁴.
d) Trocando o m=n (por que não tenho o "m" como expoente)
[2xⁿ⁺³.(1/2)xⁿ⁻¹ - 4xⁿ⁺².(1/2)xⁿ⁻¹ - 3xⁿ⁺¹.(1/2)xⁿ⁻¹ - 2xⁿ.(1/2)xⁿ⁻¹] + [2xⁿ⁺³.(-1/4)xⁿ⁻² - 4xⁿ⁺².(-1/4)xⁿ⁻² - 3xⁿ⁺¹.(-1/4)xⁿ⁻² - 2xⁿ.(-1/4)xⁿ⁻²] + [2xⁿ⁺³.xⁿ⁻³ - 4xⁿ⁺².xⁿ⁻³ - 3xⁿ⁺¹.xⁿ⁻³ - 2xⁿ.xⁿ⁻³] =
[x²ⁿ⁺² - 2x²ⁿ⁺¹ - (3/2)x²ⁿ - x²ⁿ⁻¹] + [(-1/2)x²ⁿ⁺¹ + x²ⁿ + (3/4)x²ⁿ⁻¹ + xⁿ.(1/2)x²ⁿ⁻²] + [2x²ⁿ - 4x²ⁿ⁻¹ - 3x²ⁿ⁻¹ - 2x²ⁿ⁻³] =
Obs: xⁿ⁺³.xⁿ⁻¹ = n + 3 + n - 1 = 2n + 2.