Question

(6x-x^2)^2-x^2(x-1)(x+1)+6x(3+2x^2) УПРОСТИТЬ ВЫРАЖЕНИЕ ПОЛНЫЙ ОТВЕТ ПЖЛСТ

Answer 1

(6x-x^2)^2-x^2(x-1)(x+1)+6x(3+2x^2)=

= 36х²-12х³+х⁴-х⁴-х³+х³+х² +18х+12х³= 37х²+18х=х*(37х+18)

Answer 2

Ответ....................

Answer 3

Simplifying the Expression

To simplify the given expression (6x-x^2)^2-x^2(x-1)(x+1)+6x(3+2x^2), we can follow these steps:

1. Expand the squared term (6x-x^2)^2. 2. Expand the product -x^2(x-1)(x+1). 3. Expand the product 6x(3+2x^2). 4. Combine like terms.

Step 1: Expand the Squared Term

The squared term (6x-x^2)^2 can be expanded as follows: ``` (6x-x^2)^2 = (6x-x^2)(6x-x^2) = 36x^2 - 6x^3 - 6x^3 + x^4 = x^4 - 12x^3 + 36x^2 ```

Step 2: Expand the Product

The product -x^2(x-1)(x+1) can be expanded as follows: ``` -x^2(x-1)(x+1) = -x^2(x^2 - 1) = -x^4 + x^2 ```

Step 3: Expand the Product

The product 6x(3+2x^2) can be expanded as follows: ``` 6x(3+2x^2) = 18x + 12x^3 ```

Step 4: Combine Like Terms

Now, we can combine the expanded terms: ``` (x^4 - 12x^3 + 36x^2) - x^4 + x^2 + 18x + 12x^3 = -12x^3 + 36x^2 - x^4 + x^2 + 18x + 12x^3 = 36x^2 - x^4 + x^2 + 18x = 37x^2 - x^4 + 18x ```

Therefore, the simplified expression is 37x^2 - x^4 + 18x.

Final Answer

The simplified expression of (6x-x^2)^2-x^2(x-1)(x+1)+6x(3+2x^2) is 37x^2 - x^4 + 18x.