Question

(2x − 5)²(x − 5) = (2x − 5)(x − 5)²

Answer 1

Ответ:

решение смотри на фотографии

Пошаговое объяснение:

Answer 2

Let's simplify the given equation step by step:

(2x - 5)²(x - 5) = (2x - 5)(x - 5)²

Expanding the left side of the equation using the distributive property:

(4x² - 20x + 25)(x - 5) = (2x - 5)(x - 5)²

Next, let's simplify the right side of the equation:

(x - 5)² = (x - 5)(x - 5)

Now we can rewrite the equation:

(4x² - 20x + 25)(x - 5) = (2x - 5)(x - 5)(x - 5)

Expanding both sides of the equation:

4x³ - 20x² + 25x - 20x² + 100x - 125 = 2x³ - 5x² - 5x² + 25x + 25x - 125

Combining like terms:

4x³ - 40x² + 125x - 125 = 2x³ - 10x² + 50x - 125

Now, let's simplify further by moving all terms to one side:

4x³ - 40x² + 125x - 125 - 2x³ + 10x² - 50x + 125 = 0

2x³ - 30x² + 75x = 0

Finally, we can divide the entire equation by 5 to simplify it further:

2x² - 30x + 75 = 0

So the simplified form of the equation (2x - 5)²(x - 5) = (2x - 5)(x - 5)² is 2x² - 30x + 75 = 0.