Разложите на множители:
а) $a^3 + a^2 - a - 1$;
б) $b^2 - bc - a^2 + ac$;
в) $ab^2 + cd^2 - ad^2 - b^2c$;
г) $x^2y^2 + 1 - y^2 - x^2$.
$a^3 + a^2 - a - 1 = (a^3 + a^2) - (a + 1) = a^2(a + 1) - (a + 1) = (a + 1)(a^2 - 1) = (a + 1)(a - 1)(a + 1) = (a + 1)^2(a - 1)$
$b^2 - bc - a^2 + ac = (b^2 - a^2) - (bc - ac) = (b - a)(b + a) - c(b - a) = (b - a)(b + a - c)$
$ab^2 + cd^2 - ad^2 - b^2c = (ab^2 - b^2c) + (cd^2 - ad^2) = b^2(a - c) + d^2(c - a) = b^2(a - c) - d^2(a - c) = (a - c)(b^2 - d^2) = (a - c)(b - d)(b + d)$
$x^2y^2 + 1 - y^2 - x^2 = (x^2y^2 - x^2) - (y^2 - 1) = x^2(y^2 - 1) - (y^2 - 1) = (y^2 - 1)(x^2 - 1) = (y - 1)(y + 1)(x - 1)(x + 1)$
Пожауйста, оцените решение
