Разложите на множители:
а) $a^2 - b^2 + 2(a + b)^2$;
б) $b^2 - c^2 - 10(b - c)^2$;
в) $2(x - y)^2 + 3x^2 - 3y^2$;
г) $5a^2 - 5 - 4(a + 1)^2$.
$a^2 - b^2 + 2(a + b)^2 = (a - b)(a + b) + 2(a + b)^2 = (a + b)(a - b + 2a + 2b) = (a + b)(3a + b)$
$b^2 - c^2 - 10(b - c)^2 = (b - c)(b + c) - 10(b - c)^2 = (b - c)(b + c - 10b + 10c) = (b - c)(11c - 9b)$
$2(x - y)^2 + 3x^2 - 3y^2 = 2(x - y)^2 + 3(x^2 - y^2) = 2(x - y)^2 + 3(x - y)(x + y) = (x - y)(2x - 2y + 3x + 3y) = (x - y)(5x + y)$
$5a^2 - 5 - 4(a + 1)^2 = 5(a^2 - 1) - 4(a + 1)^2 = 5(a + 1)(a - 1) - 4(a + 1)^2 = (a + 1)(5a - 5 - 4a - 4) = (a + 1)(a - 9)$
Пожауйста, оцените решение
