Question

(2а-b)³-(2a+b)³ разложите многочлен на множетели

Answer 1

Решение смотри на фото

Answer 2

Simplifying the Expression

To simplify the expression (2a-b)³-(2a+b)³, we can expand the cubes and then combine like terms. Let's break it down step by step:

Step 1: Expand the cubes using the formula (a-b)³ = a³ - 3a²b + 3ab² - b³.

For (2a-b)³, we have: (2a-b)³ = (2a)³ - 3(2a)²b + 3(2a)b² - b³ = 8a³ - 12a²b + 6ab² - b³..

For (2a+b)³, we have: (2a+b)³ = (2a)³ + 3(2a)²b + 3(2a)b² + b³ = 8a³ + 12a²b + 6ab² + b³..

Step 2: Subtract (2a+b)³ from (2a-b)³.

(2a-b)³ - (2a+b)³ = (8a³ - 12a²b + 6ab² - b³) - (8a³ + 12a²b + 6ab² + b³).

When we subtract, the terms with the same variables cancel each other out: (8a³ - 8a³) + (-12a²b - 12a²b) + (6ab² - 6ab²) + (-b³ - b³) = -24a²b - 2b³.

Therefore, the simplified expression is -24a²b - 2b³.

Factoring the Polynomial

To factor the polynomial -24a²b - 2b³, we can look for common factors and use the distributive property to factor out the greatest common factor.

In this case, the greatest common factor is -2b. Factoring it out, we get:

-24a²b - 2b³ = -2b(12a² + b²).

Therefore, the factored form of the polynomial is -2b(12a² + b²).

I hope this helps! Let me know if you have any further questions.