Question

(x-2)3+(x+2)3=2x(x2-1)3

Answer 1

3 в степенях стоят или как?

Answer 2

Let's simplify the given equation step by step:

Expanding the left side: (x - 2)³ + (x + 2)³

Using the formula for expanding the cube of a binomial (a + b)³ = a³ + 3a²b + 3ab² + b³:

= (x³ - 3x²(2) + 3x(2)² - 2³) + (x³ + 3x²(2) + 3x(2)² + 2³)

= (x³ - 6x² + 12x - 8) + (x³ + 6x² + 12x + 8)

= 2x³ + 12x² + 24x

Now, let's simplify the right side of the equation: 2x(x² - 1)³

Using the formula for expanding the cube of a binomial (a - b)³ = a³ - 3a²b + 3ab² - b³:

= 2x(x²³ - 3x²(1) + 3x(1)² - 1³)

= 2x(x³ - 3x² + 3x - 1)

Now, we can rewrite the equation as:

2x³ + 12x² + 24x = 2x(x³ - 3x² + 3x - 1)

Distributing the 2x on the right side: 2x³ + 12x² + 24x = 2x⁴ - 6x³ + 6x² - 2x

Moving all terms to one side: 2x³ + 12x² + 24x - 2x⁴ + 6x³ - 6x² + 2x = 0

Rearranging the terms: -2x⁴ + (2x³ + 6x³) + (12x² - 6x²) + (24x + 2x) = 0

Combining like terms: -2x⁴ + 8x³ + 6x² + 26x = 0

This is the simplified form of the given equation: -2x⁴ + 8x³ + 6x² + 26x = 0