Question

Представьте многочлен в виде произведения 1)х^3+3x^2+3x+9 2)x^2+xy+2x+2y 3)m^2+mn-5m-5n 4)a^2-ab-3a+3b 5)10ay-5by+2ax-bx

Answer 1

1) (x³ + 3x²) + (3x + 9) = x²(x + 3) + 3(x + 3) = (x² + 3)(x + 3)

2) x² + xy + 2x + 2y = (x² + 2x) + (xy + 2y) = x(x + 2) + y(x + 2) = (x + y)(x + 2)

3) m² + mn - 5m - 5n = (m² - 5m) + (mn - 5n) = m(m - 5) + n(m - 5) = (m + n)(m - 5)

4) a² - ab - 3a + 3b = (a²  - 3a) + (-ab + 3b) = a(a - 3) - b(a - 3) = (a - b)(a - 3)

5) (10ay - 5by) + (2ax - bx) = 5y(2a - b) + x(2a - b) = (5y + x)(2a - b)