Question

completa Los recuadros para que las siguientes igualdades sean ciertas

Answer 1

Tenemos.

Suma y resta de cubos.
Aplicas.
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)

8x³ + 27 =
2³x³ + 3³ =
(2x + 3)((2x)² - (2x)(3) + 3²)
(2x + 3)(2²x² - 6x + 9)
(2x + 3)(4x² - 6x + 9)

c¹⁵ - 216a⁶
(c⁵)³ - 6³(a²)³ =
(c⁵ - 6a²)((c⁵)² + c⁵ . 6a² + (6a²)²)
(c⁵ - 6a²)(c¹⁰ + 6c⁵a² + 6²a⁴)
(c⁵ - 6a²)(c¹⁰ + 6c⁵a² + 36a⁴)


64g¹² - b⁶ =
2⁶a¹² - b⁶ =
(2²)³(g⁴)³ - (b²)³ =
(2²g⁴ - b²)((2²g⁴)² + 2²g⁴b² + (b²)²) =
(4g⁴ - b²)(2⁴g⁸ + 4g⁴b² + b⁴) =
(4g⁴ - b²)(16g⁸ + 4g⁴b² + b⁴)

8x³ - 27 =
2³x³ - 3³ =
(2x - 3)((2x)² + (2x)(3) + 3²) =
(2x - 3)(2²x² + 6x + 9)
(2x - 3)(4x²  + 6x + 9)


C¹⁵ + 216a⁶ =
(c⁵)³ +  6³(a²)³ =
(c⁵ + 6a²)((c⁵)² - c⁵(6a²)  + (6a²)²) =
(c⁵ + 6a²)(c¹⁰ - 6c⁵a² + 6²a⁴)
(c⁵ + 6a²)(c¹⁰ - 6c⁵a² + 36a⁴)

Answer 2

Respuesta:

8x³ + 27 =

2³x³ + 3³ =

(2x + 3)((2x)² - (2x)(3) + 3²)

(2x + 3)(2²x² - 6x + 9)

(2x + 3)(4x² - 6x + 9)

c¹⁵ - 216a⁶

(c⁵)³ - 6³(a²)³ =

(c⁵ - 6a²)((c⁵)² + c⁵ . 6a² + (6a²)²)

(c⁵ - 6a²)(c¹⁰ + 6c⁵a² + 6²a⁴)

(c⁵ - 6a²)(c¹⁰ + 6c⁵a² + 36a⁴)

64g¹² - b⁶ =

2⁶a¹² - b⁶ =

(2²)³(g⁴)³ - (b²)³ =

(2²g⁴ - b²)((2²g⁴)² + 2²g⁴b² + (b²)²) =

(4g⁴ - b²)(2⁴g⁸ + 4g⁴b² + b⁴) =

(4g⁴ - b²)(16g⁸ + 4g⁴b² + b⁴)

8x³ - 27 =

2³x³ - 3³ =

(2x - 3)((2x)² + (2x)(3) + 3²) =

(2x - 3)(2²x² + 6x + 9)

(2x - 3)(4x²  + 6x + 9)

C¹⁵ + 216a⁶ =

(c⁵)³ +  6³(a²)³ =

(c⁵ + 6a²)((c⁵)² - c⁵(6a²)  + (6a²)²) =

(c⁵ + 6a²)(c¹⁰ - 6c⁵a² + 6²a⁴)

(c⁵ + 6a²)(c¹⁰ - 6c⁵a² + 36a⁴)