Разложите многочлен на множители:
а) $x^2 - y^2 - 10x - 12y - 11$;
б) $x^2 - y^2 + 8x + 10y - 9$;
в) $4x^2 - y^2 - 4x - 6y - 8$;
г) $x^2 - 4y^2 + 10x + 4y + 24$.
$x^2 - y^2 - 10x - 12y - 11 = (x^2 - 10x + 25) - (y^2 + 12y + 36) = (x - 5)^2 - (y + 6)^2 = (x - 5 - (y + 6))(x - 5 + y + 6) = (x - 5 - y - 6)(x + y + 1) = (x - y - 11)(x + y + 1)$
$x^2 - y^2 + 8x + 10y - 9 = (x^2 + 8x + 16) - (y^2 - 10y + 25) = (x + 4)^2 - (y - 5)^2 = (x + 4 - (y - 5))(x + 4 + y - 5) = (x + 4 - y + 5)(x + y - 1) = (x - y + 9)(x + y - 1)$
$4x^2 - y^2 - 4x - 6y - 8 = (4x^2 - 4x + 1) - (y^2 + 6y + 9) = (2x - 1)^2 - (y + 3)^2 = (2x - 1 - (y + 3))(2x - 1 + y + 3) = (2x - 1 - y - 3)(2x + y + 2) = (2x - y - 4)(2x + y + 2)$
$x^2 - 4y^2 + 10x + 4y + 24 = (x^2 + 10x + 25) - (4y^2 - 4y + 1) = (x + 5)^2 - (2y - 1)^2 = (x + 5 - (2y - 1))(x + 5 + 2y - 1) = (x + 5 - 2y + 1)(x + 2y + 4) = (x - 2y + 6)(x + 2y + 4)$
Пожауйста, оцените решение
