已知a的平方-b的平方=4,a的平方-c的平方=2,求代数式(a+b)乘(a+c)(b+c)(a-b)(a-c)(b-c

因为 a² - b² = 4 ,a² - c² = 2
所以 (a² - c²) - (a² - b²) = -2 ,即 b² - c² = -2
(a + b)(a + c)(b + c)(a - b)(a - c)(b - c)
= [(a + b)(a - b)] × [(b + c)(b - c)] × [(a + c)(a - c)]
= (a² - b²) × (b² - c²) × (a² - c²)
= 4 × (-2) × 2
= -16