Question

(6x – x²)² – x² (x - 1) (x + 1) + 6x (3 + 2x2)​

Answer 1

Ответ:

решено, если что обращайся

Answer 2

To simplify the expression (6x - x²)² - x² (x - 1) (x + 1) + 6x (3 + 2x²), follow these steps:

1. Expand each term separately:

   • First, square the binomial (6x - x²)²: (6x - x²)² = (6x - x²)(6x - x²)

   • Next, expand the product of x² (x - 1) (x + 1): x² (x - 1) (x + 1) = x² (x² - 1)

   • Finally, expand the product of 6x and (3 + 2x²): 6x (3 + 2x²) = 18x + 12x³

2. Apply the distributive property and combine like terms in each expression:

   • For the first expression (6x - x²)²: (6x - x²)(6x - x²) = 36x² - 6x³ - 6x³ + x⁴ = x⁴ - 12x³ + 36x²

   • For the second expression x² (x² - 1): x² (x² - 1) = x⁴ - x²

   • For the third expression 6x (3 + 2x²): 6x (3 + 2x²) = 18x + 12x³

3. Now, put all three simplified expressions back together:

   (x⁴ - 12x³ + 36x²) - (x⁴ - x²) + (18x + 12x³)

4. Combine like terms:

   x⁴ - 12x³ + 36x² - x⁴ + x² + 18x + 12x³

5. Simplify further:

   (x⁴ - x⁴) + (-12x³ + 12x³) + (36x² + x²) + 18x

6. After simplifying, you get:

   0 + 0 + 37x² + 18x

7. So, the final simplified expression is:

   37x² + 18x