Question

(2x-3)³=? (3a²+2b³)³=? ​

Answer 1

Ответ:

(2х-3)³=(2х-3)(2х-3)(2х-3)=8х³-36х²+54х-27

Объяснение:

(3а²+2b³)³=(3а²+2b³)(3а²+2b³)(3а²+2b³)=27x⁶+54b³x⁴+36b⁶x²+8b⁹

Answer 2

To find the cube of the expressions (2x - 3) and (3a² + 2b³), you can use the formula for cubing a binomial, which is:

(a - b)³ = a³ - 3a²b + 3ab² - b³

1. For (2x - 3)³:

a = 2x b = 3

(2x - 3)³ = (2x)³ - 3(2x)²(3) + 3(2x)(3)² - (3)³ (2x - 3)³ = 8x³ - 36x² + 54x - 27

So, (2x - 3)³ = 8x³ - 36x² + 54x - 27.

2. For (3a² + 2b³)³:

a = 3a² b = 2b³

(3a² + 2b³)³ = (3a²)³ - 3(3a²)²(2b³) + 3(3a²)(2b³)² - (2b³)³ (3a² + 2b³)³ = 27a^6 - 18a^4b^3 + 36a^2b^6 - 8b^9

So, (3a² + 2b³)³ = 27a^6 - 18a^4b^3 + 36a^2b^6 - 8b^9.

Answer 3

To find the cube of the expressions (2x - 3)³ and (3a² + 2b³)³, you can use the binomial expansion formula.

The binomial expansion formula for (a - b)³ is as follows:

(a - b)³ = a³ - 3a²b + 3ab² - b³

So, for (2x - 3)³:

(2x - 3)³ = (2x)³ - 3(2x)²(3) + 3(2x)(3)² - 3³ (2x - 3)³ = 8x³ - 36x² + 54x - 27

And for (3a² + 2b³)³:

(3a² + 2b³)³ = (3a²)³ + 3(3a²)²(2b³) + 3(3a²)(2b³)² + (2b³)³ (3a² + 2b³)³ = 27a^6 + 54a^4b^3 + 36a^2b^6 + 8b^9

So, the cube of (2x - 3) is 8x³ - 36x² + 54x - 27, and the cube of (3a² + 2b³) is 27a^6 + 54a^4b^3 + 36a^2b^6 + 8b^9.