Question

Разложите на множители 1) x²-25 2) ab²-ac² 3) -3a²-6ab-3b²

Answer 1

1) х^2 - 5^2 = (x - 5)(x + 5)
2) a(b^2 - c^2) = a(b-c)(b+c)
3) - 3(a^2 + 2ab + b^2) = - 3(a +b)(a+b)

Answer 2

1. x² - 25 can be factored using the difference of squares formula: x² - 25 = (x - 5)(x + 5)

2. For ab² - ac², we can factor out the common factor "a": ab² - ac² = a(b² - c²)

3. To factor -3a² - 6ab - 3b², we can first factor out -3: -3a² - 6ab - 3b² = -3(a² + 2ab + b²)

   Then, we can recognize that a² + 2ab + b² is a perfect square, which can be factored as (a + b)²: -3(a² + 2ab + b²) = -3(a + b)²

Therefore, the factored forms are:

1. x² - 25 = (x - 5)(x + 5)
2. ab² - ac² = a(b² - c²)
3. -3a² - 6ab - 3b² = -3(a + b)²