Разложите на множители многочлен:
1) $x^2 - 6xy + 5y^2$;
2) $a^2 + 5ab - 36b^2$;
3) $3m^2 - 8mn - 3n^2$;
4) $4x^2 - 5xy + y^2$.
$x^2 - 6xy + 5y^2 = x^2 - xy - 5xy + 5y^2 = (x^2 - xy) - (5xy - 5y^2) = x(x - y) - 5y(x - y) = (x - y)(x - 5y)$
$a^2 + 5ab - 36b^2 = a^2 + 9ab - 4ab - 36b^2 = (a^2 + 9ab) - (4ab + 36b^2) = a(a + 9b) - 4b(a + 9b) = (a + 9b)(a - 4b)$
$3m^2 - 8mn - 3n^2 = 3m^2 + mn - 9mn - 3n^2 = (3m^2 + mn) - (9mn + 3n^2) = m(3m + n) - 3n(3m + n) = (3m + n)(m - 3n)$
$4x^2 - 5xy + y^2 = 4x^2 - xy - 4xy + y^2 = (4x^2 - xy) - (4xy - y^2) = x(4x - y) - y(4x - y) = (4x - y)(x - y)$
Пожауйста, оцените решение
