Question

diferencia de cubos
xfa

Answer 1

El resultado para cada operación sera:

• 8x³ + 1 = (2x + 1)*(4x² - 2x + 1)

• 27 - 8a³ = (3 - 2a)*(4 +5a + 4a²)

• 27x³ + 8 = (3x + 2)*(9x² - 6x + 4)

• 64a³ - 27b³ =  ( 4a - 3b)*(16a² + 12ab + 9b²)

• 125n³ + 64 = (5n + 4)*(25² - 25n + 16)

• 216a³b³ + 1000 =  (6ab + 10)*(36a²b² - 60ab + 100)

• x⁶ - y ⁶ = (x + y)*(x-y)*(x⁴ + x²*y² + y⁴)

• 125a⁶ + 512b⁶ = ( 5a² + 8b²)*(5a⁴ - 40a²b² + 64b⁴)

• x⁹ + 8y⁹ = (x³ + 2y³)*(x³ - y³)²

• x⁹ + 8y⁹ = (x³ + 2y³)*(x³ - y³)²

La suma o diferencia de cubos de dos números a y b es:

a³ + b³ = (a + b)*(a² - ab + b²)

a³ - b³ = (a - b)*(a² + ab + b²)

La resta de cuadrados:

a² - b² = (a + b)*(a -b)

Además

(a - b) ² = a² - 2ab + b²

Procedemos a resolver para cada caso:

• 8x³ + 1 = (2x)³ + 1³ = (2x + 1)*((2x)² - 2x*1 + 1²)

= (2x + 1)*(4x² - 2x + 1)

• 27 - 8a³ = (3)³ - (2a)³ = (3 - 2a)*((2)² +3*2a + (2a)²)

= (3 - 2a)*(4 +5a + 4a²)

• 27x³ + 8 = (3x)³ + 2³ = (3x + 2)*((3x)² - 3x*2 + 2²)

= (3x + 2)*(9x² - 6x + 4)

• 64a³ - 27b³ = (4a)³ - (3b)³ = ( 4a - 3b)*((4a)² + 4a*3b + (3b)²)

= ( 4a - 3b)*(16a² + 12ab + 9b²)

• 125n³ + 64 = (5n)³ + 4³ = (5n + 4)*((5n)² - 5n*5 + 4²)

= (5n + 4)*(25² - 25n + 16)

• 216a³b³ + 1000 =  (6ab)³ + 10³ = (6ab + 10)*((6ab)² - 6ab*10 + 10²)

= (6ab + 10)*(36a²b² - 60ab + 100)

• x⁶ - y ⁶ = (x²)³ - (y²)³ = ( x² - y²)*((x²)² + x²*y² + (y²)²)

= ( x² - y²)*(x⁴ + x²*y² + y⁴)

= (x + y)*(x-y)*(x⁴ + x²*y² + y⁴)

• 125a⁶ + 512b⁶ = (5a²)³ + (8b²)³ = ( 5a² + 8b²)*((5a²)² - 5a²*8b² + (8b²)²)

= ( 5a² + 8b²)*(5a⁴ - 40a²b² + 64b⁴)

• x⁹ + 8y⁹ = (x³)³ + (2y³)³ = (x³ + 2y³)*((x³)² - x³*2y³ + (y³)²)

= (x³ + 2y³)*(x⁶ - 2x³y³ + y⁶) = (x³ + 2y³)*(x³ - y³)²

• x⁹ + 8y⁹ = (x³)³ + (2y³)³ = (x³ + 2y³)*((x³)² - x³*2y³ + (y³)²)

= (x³ + 2y³)*(x⁶ - 2x³y³ + y⁶) = (x³ + 2y³)*(x³ - y³)²