4ab+9-4a²-b² 1-a²+b²-a²b² 4x+8y-xy-y²-16 a²-ab-2a+b+1 x.y為整數，x²+y²+4x+4=0,3x+y為多少？

4ab + 9 - 4a² - b²
= 9 - 4a² + 4ab - b²
= 9 - (4a² - 4ab + b²)
= 3² - (2a - b)²
= (3 + 2a - b)(3 - 2a + b)

1 - a² + b² - a²b²
= (1 - a²) + b²(1 - a²)
= (1 - a²)(1 + b²)
= (1 + a)(1 - a)(1 + b²)

4x + 8y - xy - y² - 16
= (4x - xy) - (16 - 8y + y²)
= x(4 - y) - (4 - y)²
= (4 - y)(x - 4 + y)
= (4 - y)(x + y - 4)

a² - ab - 2a + b + 1
= (a² - 2a + 1) - (ab - b)
= (a - 1)² - b(a - 1)
= (a - 1)(a - b - 1)

x² + y² + 4x + 4 = 0
==> (x² + 4x + 4) + y² = 0
==> (x + 2)² + y² = 0
所以 x = -2, y = 0 (任何整數的平方都是大過或等於 0 的)
所以
3x + y
= 3(-2) + 0
= -6