Представьте в виде произведения выражения:
1) $(5x - y^2)(5x + y^2) - 2(15x - 7y^2) - 40$;
2) $(3m - 2n)(12m + 5n) + 3m(3n + 4) - 2(3n^2 - 20n + 12)$.
$(5x - y^2)(5x + y^2) - 2(15x - 7y^2) - 40 = 25x^2 - y^4 - 30x + 14y^2 - 40 = 25x^2 - y^4 - 30x + 14y^2 - 49 + 9 = (25x^2 - 30x + 9) - (y^4 - 14y^2 + 49) = (5x - 3)^2 - (y^2 + 7)^2 = (5x - 3 - y^2 - 7)(5x - 3 + y^2 + 7) = (5x - y^2 - 10)(5x + y^2 + 4)$
$(3m - 2n)(12m + 5n) + 3m(3n + 4) - 2(3n^2 - 20n + 12) = 36m^2 - 24mn + 15mn - 10n^2 + 9mn + 12m - 6n^2 + 40n - 24 = 36m^2 - 16n^2 + 12m + 40n - 24 = 36m^2 - 16n^2 + 12m + 40n - 25 + 1 = (36m^2 + 12m + 1) - (16n^2 - 40n + 25) = (6m + 1)^2 - (4n - 5)^2 = (6m + 1 - 4n + 5)(6m + 1 + 4n - 5) = (6m - 4n + 6)(6m + 4n - 4) = 2(3m - 2n + 3)2(3m + 2n - 2) = 4(3m - 2n + 3)(3m + 2n - 2)$
Пожауйста, оцените решение
