Question

Разложите на множители.

1) 7х³ - 28х

2) 5а² - 10 ab + 5b²

3) x³ - 8

5) x³ - y³ -5x (x² + xy + y²)

Answer 1

1) 7x³ - 28x = 7x(x² - 4) = 7x(x + 2)(x - 2)

2) 5a² - 10ab + 5b² = 5(a² - 2ab + b²) = 5(a - b)² = 5(a - b)(a - b)

3) x³ - 8 = x³ - 2³ = (x - 2)(x² + 2x + 4)

4) x³ - y³ - 5x(x² + xy + y²) = (x - y)(x² + xy + y²) - 5x(x² + xy + y²) =
= (x² + xy + y²)(x - y - 5x) = (x² + xy + y²)(- 4x - y) = - (4x + y)(x² + xy + y²)