第1章 1.30

(1)

$2xy + ab + 2ay + bx = x(b + 2y) + a(b + 2y) = (b + 2y)(x + a)$

(2)

$ab - bc + ca - b^2 = a(b + c) - b(b + c) = (b + c)(a - b)$

(3)

$x^2y + x^2 - y - 1 = x^2(y + 1) - (y + 1) = (y + 1)(x^2 - 1) = (y + 1)(x - 1)(x + 1)$

(4)

$x^2y + x^2 - 2xy - 4 = xy(x - 2) + (x - 2)(x + 2) = (x - 2)(xy + x + 2)$

(5)

$x^3 + 2x^2y - 9x - 18y = x^2(x + 2y) - 9(x + 2y) = (x + 2y)(x^2 - 9) = (x + 2y)(x - 3)(x + 3)$

(6)

$x^2 + 2xy + y^2 - 2x - 2y - 3 = (x + y)^2 - 2(x + y) - 3 = \{(x + y) - 3\}\{(x + y) + 1\}$

(7)

$a^2 - 2b^2 + ab + 2a + 7b - 3 = (a + 2b)(a - b) + 2a + 7b - 3 = \{(a + 2b) - 1\}\{(a - b) + 3\}$

(8)

$2x^2 + 3xy - 2y^2 + x + 7y - 3 = (2x - y)(x + 2y) + x + 7y - 3 = \{(x + 2y) - 1\}\{(2x - y) + 3\}$